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arxiv: 2512.10101 · v2 · submitted 2025-12-10 · 🧮 math-ph · cond-mat.stat-mech· hep-th· math.MP· math.OA· math.QA

The von Neumann algebraic quantum group SU_q(1,1)rtimes mathbb{Z}₂ and the DSSYK model

Koen Schouten , Mikhail Isachenkov This is my paper

Pith reviewed 2026-05-16 22:45 UTC · model grok-4.3

classification 🧮 math-ph cond-mat.stat-mechhep-thmath.MPmath.OAmath.QA
keywords DSSYK modelquantum groupsvon Neumann algebrasAdS2q-deformationSYKquantum homogeneous spacesnormaliser
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The pith

Dynamics on quantum AdS2,q reduce to the DSSYK model using the von Neumann algebraic quantum group SU_q(1,1) extended by Z2.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper constructs a von Neumann algebraic quantum group description of the DSSYK model. It builds the quantum Gauss decomposition for SU_q(1,1) ⋊ Z2 and derives the Casimir action on quantum homogeneous spaces. The dynamics on quantum AdS2,q are shown to reduce to those of the DSSYK model exclusively at the level of this normaliser extension. The framework also restricts quantised coordinates to ensure length positivity and non-negative integer chord numbers while connecting strange series representations to AdS-dS interpolation.

Core claim

The operator-algebraic quantum Gauss decomposition is constructed for the von Neumann algebraic quantum group SU_q(1,1)⋊Z2, which is the q-deformation of the normaliser of SU(1,1) in SL(2,C). The Casimir action on its quantum homogeneous spaces is derived. The dynamics on quantum AdS2,q space are shown to reduce to that of the DSSYK model. This reduction works exclusively at the level of the normaliser, which is necessary for a consistent definition of the locally compact quantum group. The description gives a natural restriction on the allowed quantised coordinates, ensuring length positivity and non-negative integer chord numbers. Remarks are made on the correlation function related to the

What carries the argument

The von Neumann algebraic quantum group SU_q(1,1) ⋊ Z2, its quantum Gauss decomposition, and the Casimir action on quantum homogeneous spaces.

Load-bearing premise

The reduction of the dynamics on quantum AdS2,q to the DSSYK model occurs exclusively at the level of the normaliser SU_q(1,1) ⋊ Z2 and this extension is necessary for consistent definition of the locally compact quantum group.

What would settle it

A calculation of the correlation functions using the Casimir action on the quantum homogeneous spaces of SU_q(1,1) ⋊ Z2 that fails to reproduce the DSSYK correlators would disprove the reduction.

read the original abstract

The double-scaling limit of the SYK (DSSYK) model is known to possess an underlying $\mathcal{U}_q(\mathfrak{su}(1,1))$ quantum group symmetry. In this paper, we provide, for the first time, a von Neumann algebraic quantum group-theoretical description of the degrees of freedom and the dynamics of the DSSYK model. In particular, we construct the operator-algebraic quantum Gauss decomposition for the von Neumann algebraic quantum group $\mathrm{SU}_q(1,1)\rtimes \mathbb{Z}_2$, i.e. the $q$-deformation of the normaliser of $\mathrm{SU}(1,1)$ in $\mathrm{SL}(2,\mathbb{C})$, and derive the Casimir action on its quantum homogeneous spaces. We then show that the dynamics on quantum AdS$_{2,q}$ space reduces to that of the DSSYK model. Furthermore, we argue that the extension of the global symmetry group to its normaliser is not only necessary for a consistent definition of the locally compact quantum group, but that, moreover, the reduction to the DSSYK model works exclusively at the level of the normaliser. The von Neumann algebraic description is shown to give a natural restriction on the allowed quantised coordinates, elegantly ensuring length positivity and non-negative integer chord numbers. Lastly, we make remarks on the correlation function related to the strange series representation, which is argued to interpolate between the AdS and dS regions of our $q$-homogeneous space.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 3 minor

Summary. The manuscript constructs the von Neumann algebraic quantum group SU_q(1,1) ⋊ Z_2 as the q-deformation of the normalizer of SU(1,1) in SL(2,C). It provides an operator-algebraic quantum Gauss decomposition, derives the Casimir operator action on the associated quantum homogeneous spaces, and shows that the dynamics on quantum AdS_{2,q} reduce to the DSSYK model. The paper argues that the Z_2 extension is necessary both for consistency of the locally compact quantum group and for the exclusivity of the DSSYK reduction. It further notes that the construction imposes natural restrictions on quantized coordinates ensuring length positivity and non-negative integer chord numbers, and includes remarks on correlation functions from the strange series representation that interpolate between AdS and dS regions.

Significance. If the derivations are rigorous and the reduction is independently derived rather than arranged by construction, the work would supply a concrete von Neumann algebraic quantum-group foundation for the DSSYK model, linking its Hamiltonian and chord spectrum directly to the Casimir action on a q-deformed homogeneous space. The emphasis on the normalizer extension, positivity constraints, and interpolation between AdS and dS regions addresses longstanding issues in quantizing AdS_2 and could strengthen holographic interpretations of double-scaled SYK. The provision of an explicit operator-algebraic Gauss decomposition is a technical strength that may enable further computations in related models.

major comments (2)
  1. [Abstract and §4] Abstract and §4 (Casimir action on quantum homogeneous spaces): The central claim that the DSSYK reduction occurs exclusively for the normaliser SU_q(1,1) ⋊ Z_2 requires an explicit side-by-side computation showing that the Casimir operator restricted to the quantum homogeneous space of the non-extended SU_q(1,1) fails to reproduce the DSSYK Hamiltonian and chord-number spectrum. The manuscript asserts necessity of the extension but supplies no such contrasting derivation, leaving the exclusivity statement unsupported.
  2. [§3 and §5] §3 (quantum Gauss decomposition) and §5 (reduction to DSSYK): The identification of the Casimir action with the DSSYK dynamics is presented after constructing the extended group, but the text does not demonstrate that the same reduction cannot be obtained from the proper subgroup SU_q(1,1) alone. Without this comparison, it is impossible to rule out that the match is achieved by the choice of extension rather than derived from the quantum-group structure.
minor comments (3)
  1. [Abstract] The abstract states that the construction is given 'for the first time,' yet prior literature on the U_q(su(1,1)) symmetry of DSSYK is referenced only briefly; a short paragraph situating the novelty relative to existing quantum-group treatments of SYK would improve context.
  2. [§2] Notation for the quantum AdS_{2,q} space and its homogeneous-space coordinates is introduced in §2 but used with slight variations in later sections; a single consolidated definition or table of symbols would aid readability.
  3. [Final section] The final remarks on the strange-series correlation function are qualitative; adding at least one explicit integral or matrix-element formula would make the interpolation claim between AdS and dS regions more concrete.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough review and valuable comments on our manuscript. We address the major comments point by point below. Where appropriate, we will revise the manuscript to provide the requested clarifications and explicit comparisons.

read point-by-point responses

  1. Referee: [Abstract and §4] Abstract and §4 (Casimir action on quantum homogeneous spaces): The central claim that the DSSYK reduction occurs exclusively for the normaliser SU_q(1,1) ⋊ Z_2 requires an explicit side-by-side computation showing that the Casimir operator restricted to the quantum homogeneous space of the non-extended SU_q(1,1) fails to reproduce the DSSYK Hamiltonian and chord-number spectrum. The manuscript asserts necessity of the extension but supplies no such contrasting derivation, leaving the exclusivity statement unsupported.

    Authors: We agree that an explicit side-by-side comparison would make the exclusivity claim more robust. In the manuscript, the necessity of the Z_2 extension is motivated by the requirement for a consistent locally compact quantum group structure and by the fact that the normalizer allows the quantum homogeneous space to support the precise Casimir action matching the DSSYK Hamiltonian and non-negative chord spectrum. The non-extended SU_q(1,1) does not admit the same decomposition or positivity constraints. To address the referee's concern, we will add a short subsection or remark in §4 providing the contrasting derivation, showing explicitly that the Casimir on the non-extended space yields a different spectrum incompatible with DSSYK. revision: yes

  2. Referee: [§3 and §5] §3 (quantum Gauss decomposition) and §5 (reduction to DSSYK): The identification of the Casimir action with the DSSYK dynamics is presented after constructing the extended group, but the text does not demonstrate that the same reduction cannot be obtained from the proper subgroup SU_q(1,1) alone. Without this comparison, it is impossible to rule out that the match is achieved by the choice of extension rather than derived from the quantum-group structure.

    Authors: We acknowledge this point. The construction in §3 of the quantum Gauss decomposition is performed for the extended group because the normalizer is required for the von Neumann algebraic structure to be well-defined as a locally compact quantum group. The reduction in §5 relies on this. We will revise §5 to include an explicit argument or computation demonstrating that attempting the same reduction with only SU_q(1,1) fails to produce the DSSYK chord spectrum due to the absence of the Z_2 action, which is essential for the sign flips and positivity. This will clarify that the match is structural rather than by construction. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper constructs the von Neumann algebraic quantum group SU_q(1,1)⋊Z₂ via operator-algebraic Gauss decomposition, derives the Casimir action on its quantum homogeneous spaces, and shows that the resulting dynamics on quantum AdS_{2,q} reduce to the DSSYK model. This chain is self-contained: the group extension and Casimir operators are defined independently of the target DSSYK quantities, with the reduction following from explicit operator actions rather than presupposed fits or self-definitions. The exclusivity claim for the normaliser is asserted on consistency grounds for the locally compact quantum group but does not reduce the central derivation to a tautology or self-citation load-bearing step. No equations or steps collapse by construction to the inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The central claim rests on the existence of a von Neumann algebraic structure for the normalizer group, the definition of its quantum homogeneous spaces, and the identification of their dynamics with DSSYK; q is the key deformation parameter whose value is chosen to match the model.

free parameters (1)
  • q
    Deformation parameter of the quantum group; its specific value is selected so that the resulting dynamics reproduce the DSSYK model.
axioms (1)
  • domain assumption Existence of a consistent von Neumann algebraic quantum group structure on SU_q(1,1) ⋊ Z2
    Invoked as the foundational object whose Gauss decomposition and Casimir action are constructed.
invented entities (1)
  • quantum AdS_{2,q} space no independent evidence
    purpose: Quantum homogeneous space whose dynamics are claimed to reduce exactly to the DSSYK model
    Introduced via the quantum group construction; no independent falsifiable evidence outside the identification is provided in the abstract.

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Forward citations

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Reference graph

Works this paper leans on

150 extracted references · 150 canonical work pages · cited by 5 Pith papers · 47 internal anchors

  1. [1]

    Causal connectability between quantum systems and the black hole interior in holographic duality,

    S. Leutheusser and H. Liu. “Causal connectability between quantum systems and the black hole interior in holographic duality”,Phys. Rev. D108(2023) [arXiv:2110.05497]

    work page arXiv 2023

  2. [2]

    Emergent times in holographic duality,

    S. Leutheusser and H. Liu. “Emergent times in holographic duality”,Phys. Rev. D108 (2023) [arXiv:2112.12156]

    work page arXiv 2023

  3. [3]

    C*-Algebras and Operator Theory

    G. Murphy. “C*-Algebras and Operator Theory”. Academic Press, Inc. (1990)

    work page 1990

  4. [4]

    Theory of Operator Algebras I

    M. Takesaki. “Theory of Operator Algebras I”. Springer New York, NY (1979)

    work page 1979

  5. [5]

    van der Heijden and E

    J. van der Heijden and E. Verlinde. “An operator algebraic approach to black hole information”,Journal of High Energy Physics2025(2025) [arXiv:2408.00071]

    work page arXiv 2025

  6. [6]

    Witten,Gravity and the crossed product,JHEP10(2022) 008 [2112.12828]

    E. Witten. “Gravity and the crossed product”,Journal of High Energy Physics2022 (2022) [arXiv:2112.12828]

    work page arXiv 2022

  7. [7]

    An Algebra of Observables for de Sitter Space

    V. Chandrasekaran, R. Longo, G. Penington and E. Witten. “An algebra of observables for de Sitter space”,Journal of High Energy Physics2023(2023) [arXiv:2206.10780]

    work page internal anchor Pith review arXiv 2023

  8. [8]

    Chandrasekaran, G

    V. Chandrasekaran, G. Penington and E. Witten. “Large N algebras and generalized entropy”,Journal of High Energy Physics2023(2023) [arXiv:2209.10454]

    work page arXiv 2023

  9. [9]

    Witten,Why Does Quantum Field Theory In Curved Spacetime Make Sense? And What Happens To The Algebra of Observables In The Thermodynamic Limit?, 2112.11614

    E. Witten. “Why Does Quantum Field Theory in Curved Spacetime Make Sense? And What Happens to the Algebra of Observables in the Thermodynamic Limit?”, inDialogues Between Physics and Mathematics: C. N. Yang at 100, (eds. M.-L. Ge and Y.-H. He). pp. 241–284. Springer International Publishing (2022) [arXiv:2112.11614]

    work page arXiv 2022

  10. [10]

    Penington and E

    G. Penington and E. Witten. “Algebras and States in JT Gravity”,Preprint(2023) [arXiv:2301.07257]

    work page arXiv 2023

  11. [11]

    Sorce,Notes on the type classification of von Neumann algebras,Rev

    J. Sorce. “Notes on the type classification of von Neumann algebras”,Reviews in Mathematical Physics36(2024) 2430002 [arXiv:2302.01958]

    work page arXiv 2024

  12. [12]

    Quantum Groups and Their Representations

    A. Klimyk and K. Schm¨ udgen. “Quantum Groups and Their Representations”. Theoretical and Mathematical Physics. Springer Berlin, Heidelberg (1997)

    work page 1997

  13. [13]

    Quantum Groups

    C. Kassel. “Quantum Groups”. Springer New York, NY (2012)

    work page 2012

  14. [14]

    A Guide to Quantum Groups

    V. Chari and A. Pressley. “A Guide to Quantum Groups”. Cambridge University Press (1995)

    work page 1995

  15. [15]

    Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet

    S. Sachdev and J. Ye. “Gapless spin-fluid ground state in a random quantum Heisenberg magnet”,Phys. Rev. Lett.70(1993) 3339 [arXiv:cond-mat/9212030]

    work page internal anchor Pith review Pith/arXiv arXiv 1993

  16. [16]

    A simple model of quantum holography

    A. Kitaev. “A simple model of quantum holography”, 2015. https://online.kitp.ucsb.edu/online/entangled15/kitaev/, https://online.kitp.ucsb.edu/online/entangled15/kitaev2/

    work page 2015

  17. [17]

    Black Holes and Random Matrices

    J.S. Cotler, G. Gur-Ari, M. Hanada, J. Polchinski, P. Saad, S.H. Shenker et al.. “Black holes and random matrices”,Journal of High Energy Physics2017(2017) [arXiv:1611.04650]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  18. [18]

    Chord diagrams, exact correlators in spin glasses and black hole bulk reconstruction

    M. Berkooz, P. Narayan and J. Simon. “Chord diagrams, exact correlators in spin glasses and black hole bulk reconstruction”,Journal of High Energy Physics2018(2018) [arXiv:1806.04380]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  19. [19]

    Towards a full solution of the large N double-scaled SYK model

    B. Berkooz, M. Isachenkov, V. Narovlansky and G. Torrents. “Towards a full solution of the large N double-scaled SYK model”,Journal of High Energy Physics79(2019) [arXiv:1811.02584]. – 81 –

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  20. [20]

    Berkooz, M

    M. Berkooz, M. Isachenkov, P. Narayan and V. Narovlansky. “Quantum groups, non-commutativeAdS 2, and chords in the double-scaled SYK model”,Journal of High Energy Physics76(2023) [arXiv:2212.13668]

    work page arXiv 2023

  21. [21]

    Narovlansky and H

    V. Narovlansky and H. Verlinde. “Double-scaled SYK and de Sitter holography”,Journal of High Energy Physics2025(2025) [arXiv:2310.16994]

    work page arXiv 2025

  22. [23]

    Verlinde and M

    H. Verlinde and M. Zhang. “SYK correlators from 2D Liouville-de Sitter gravity”,Journal of High Energy Physics2025(2025) [arXiv:2402.02584]

    work page arXiv 2025

  23. [24]

    Tietto and H

    D. Tietto and H. Verlinde. “A microscopic model of de Sitter spacetime with an observer”, Preprint(2025) [arXiv:2502.03869]

    work page arXiv 2025

  24. [25]

    Okuyama, De Sitter JT gravity from double-scaled SYK , 2505.08116

    K. Okuyama. “de Sitter JT gravity from double-scaled SYK”,Journal of High Energy Physics2025(2025) [arXiv:2505.08116]

    work page arXiv 2025

  25. [26]

    Almheiri and F

    A. Almheiri and F.K. Popov. “Holography on the Quantum Disk”,Journal of High Energy Physics2024(2024) [arXiv:2401.05575]

    work page arXiv 2024

  26. [27]

    Blommaert, A

    A. Blommaert, A. Levine, T.G. Mertens, J. Papalini and K. Parmentier. “An entropic puzzle in periodic dilaton gravity and DSSYK”,Journal of High Energy Physics2025 (2025) [arXiv:2411.16922]

    work page arXiv 2025

  27. [28]

    Jt gravity with mat- ter, generalized eth, and random matri- ces

    D.L. Jafferis, D.K. Kolchmeyer, B. Mukhametzhanov and J. Sonner. “Jackiw-Teitelboim gravity with matter, generalized eigenstate thermalization hypothesis, and random matrices”,Phys. Rev. D108(2023) 066015 [arXiv:2209.02131]

    work page arXiv 2023

  28. [29]

    Susskind, Entanglement and Chaos in De Sitter Space Holography: An SYK Example , JHAP 1 (2021) 1 [ 2109.14104]

    L. Susskind. “Entanglement and Chaos in De Sitter Space Holography: An SYK Example”, Journal of Holography Applications in Physics1(2021) 1 [arXiv:2109.14104]

    work page arXiv 2021

  29. [30]

    Susskind,Scrambling in Double-Scaled SYK and De Sitter Space,2205.00315

    L. Susskind. “Scrambling in Double-Scaled SYK and De Sitter Space”,Preprint(2022) [arXiv:2205.00315]

    work page arXiv 2022

  30. [31]

    Susskind,De Sitter Space, Double-Scaled SYK, and the Separation of Scales in the Semiclassical Limit,2209.09999

    L. Susskind. “De Sitter Space, Double-Scaled SYK, and the Separation of Scales in the Semiclassical Limit”,Journal of Holography Applications in Physics5(2025) 1 [arXiv:2209.09999]

    work page arXiv 2025

  31. [32]

    Susskind,De Sitter Space has no Chords

    L. Susskind. “De Sitter Space has no Chords. Almost Everything is Confined”,Journal of Holography Applications in Physics3(2023) 1 [arXiv:2303.00792]

    work page arXiv 2023

  32. [33]

    Sekino and L

    Y. Sekino and L. Susskind. “Double-Scaled SYK, QCD, and the Flat Space Limit of de Sitter Space”,Journal of High Energy Physics2025(2025) [arXiv:2501.09423]

    work page arXiv 2025

  33. [34]

    Bhattacharjee, P

    B. Bhattacharjee, P. Nandy and T. Pathak. “Krylov complexity in large q and double-scaled SYK model”,Journal of High Energy Physics2023(2023) [arXiv:2210.02474]

    work page arXiv 2023

  34. [35]

    Blommaert, T

    A. Blommaert, T.G. Mertens and S. Yao. “Dynamical actions and q-representation theory for double-scaled SYK”,Journal of High Energy Physics2024(2024) [arXiv:2306.00941]

    work page arXiv 2024

  35. [36]

    Quantum group origins of edge states in double-scaled SYK,

    A. Belaey, T.G. Mertens and T. Tappeiner. “Quantum group origins of edge states in double-scaled SYK”,Preprint(2025) [arXiv:2503.20691]

    work page arXiv 2025

  36. [37]

    van der Heijden, E

    J. van der Heijden, E. Verlinde and J. Xu. “Quantum Symmetry and Geometry in Double-Scaled SYK”,Preprint(2025) [arXiv:2511.08743]

    work page arXiv 2025

  37. [38]

    Blommaert, T

    A. Blommaert, T.G. Mertens and S. Yao. “The q-Schwarzian and Liouville gravity”, Journal of High Energy Physics2024(2024) [arXiv:2312.00871]. – 82 –

    work page arXiv 2024

  38. [39]

    Parisi’s Hypercube, Fock-Space Frustration, and near-AdS2/near-CFT1 Holography

    M. Berkooz, Y. Jia and N. Silberstein. “Parisi’s Hypercube, Fock-Space Frustration, and near-AdS2/near-CFT1 Holography”,Physical Review Letters132(2024) [arXiv:2303.18182]

    work page arXiv 2024

  39. [40]

    Okuyama and K

    K. Okuyama and K. Suzuki. “Correlators of double scaled SYK at one-loop”,Journal of High Energy Physics2023(2023) [arXiv:2303.07552]

    work page arXiv 2023

  40. [41]

    Lin and L

    L. Susskind and H. Lin. “Infinite Temperature’s Not So Hot”,Preprint(2022) [arXiv:2206.01083]

    work page arXiv 2022

  41. [42]

    Semiclassical geometry in double-scaled SYK

    A. Goel, V. Narovlansky and H. Verlinde. “Semiclassical geometry in double-scaled SYK”, Journal of High Energy Physics2023(2023) [arXiv:2301.05732]

    work page arXiv 2023

  42. [43]

    Berkooz, N

    M. Berkooz, N. Brukner, Y. Jia and O. Mamroud. “From Chaos to Integrability in Double Scaled Sachdev-Ye-Kitaev Model via a Chord Path Integral”,Phys. Rev. Lett.133(2024) 221602 [arXiv:2403.01950]

    work page arXiv 2024

  43. [44]

    Verlinde,Double-scaled SYK, chords and de Sitter gravity,JHEP03(2025) 076 [2402.00635]

    H. Verlinde. “Double-scaled SYK, Chords and de Sitter Gravity”,Journal of High Energy Physics2025(2024) [arXiv:2402.00635]

    work page arXiv 2024

  44. [45]

    Quantum gravity of the Heisenberg algebra

    A. Almheiri, A. Goel and X.-Y. Hu. “Quantum gravity of the Heisenberg algebra”,Journal of High Energy Physics2024(2024) [arXiv:2403.18333]

    work page arXiv 2024

  45. [46]

    Bossi, L

    L. Bossi, L. Griguolo, J. Papalini, L. Russo and D. Seminara. “Sine-dilaton gravity vs double-scaled SYK: exploring one-loop quantum corrections”,Journal in High Energy Physics2025(2025) [arXiv:2411.15957]

    work page arXiv 2025

  46. [47]

    Xu, On Chord Dynamics and Complexity Growth in Double-Scaled SYK, (2024), arXiv:2411.04251 [hep-th]

    J. Xu. “On Chord Dynamics and Complexity Growth in Double-Scaled SYK”,Journal of High Energy Physics2025(2025) [arXiv:2411.04251]

    work page arXiv 2025

  47. [48]

    Heller, J

    M.P. Heller, J. Papalini and T. Schuhmann. “Krylov Spread Complexity as Holographic Complexity beyond Jackiw-Teitelboim Gravity”,Physical Review Letters135(2025) [arXiv:2412.17785]

    work page arXiv 2025

  48. [49]

    Gaiotto and H

    D. Gaiotto and H. Verlinde. “SYK-Schur duality: double scaled SYK correlators fromN= 2 supersymmetric gauge theory”,Journal of High Energy Physics2025(2025) 163 [arXiv:2409.11551]

    work page arXiv 2025

  49. [50]

    A Paradox and its Resolution Illustrate Principles of de Sitter Holography,

    L. Susskind. “A Paradox and its Resolution Illustrate Principles of de Sitter Holography”, Journal of Holography Applications in Physics5(2025) [arXiv:2304.00589]

    work page arXiv 2025

  50. [51]

    Aguilar-Gutierrez, Towards complexity in de Sitter space from the doubled-scaled Sachdev-Ye-Kitaev model, JHEP 10 (2024) 107 [ 2403.13186]

    S.E. Aguilar-Gutierrez. “Towards complexity in de Sitter space from the double-scaled Sachdev-Ye-Kitaev model”,Journal of High Energy Physics2024(2024) [arXiv:2403.13186]

    work page arXiv 2024

  51. [52]

    Aguilar-Gutierrez,T 2 deformations in the double-scaled SYK model: Stretched horizon thermodynamics,2410.18303

    S.E. Aguilar-Gutierrez. “T 2 deformations in the double-scaled SYK model: Stretched horizon thermodynamics”,Preprint(2024) [arXiv:2410.18303]

    work page arXiv 2024

  52. [53]

    Milekhin and J

    A. Milekhin and J. Xu. “Revisiting Brownian SYK and its possible relations to de Sitter”, Journal of High Energy Physics2024(2024) [arXiv:2312.03623]

    work page arXiv 2024

  53. [54]

    Comments on the Sachdev-Ye-Kitaev model

    J. Maldacena and D. Stanford. “Remarks on the Sachdev-Ye-Kitaev model”,Phys. Rev. D 94(2016) 106002 [arXiv:1604.07818]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  54. [55]

    Lower dimensional gravity

    R. Jackiw. “Lower dimensional gravity”,Nuclear Physics B252(1985) 343

    work page 1985

  55. [56]

    Gravitation and Hamiltonian structure in two spacetime dimensions

    C. Teitelboim. “Gravitation and Hamiltonian structure in two spacetime dimensions”, Physics Letters B126(1983) 41. – 83 –

    work page 1983

  56. [57]

    The Large-N Limit of Superconformal Field Theories and Supergravity

    J. Maldacena. “The Large-N Limit of Superconformal Field Theories and Supergravity”, International Journal of Theoretical Physics38(1999) 1113

    work page 1999

  57. [58]

    The World as a Hologram

    L. Susskind. “The world as a hologram”,Journal of Mathematical Physics36(1995) 6377–6396 [arXiv:hep-th/9409089]

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  58. [59]

    Anti-de Sitter Space, Thermal Phase Transition, And Confinement In Gauge Theories

    E. Witten. “Anti-de Sitter Space, Thermal Phase Transition, And Confinement In Gauge Theories”,Advances in Theoretical and Mathematical Physics2(1998) 505 [arXiv:hep-th/9803131]

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  59. [60]

    The Holographic Bound in Anti-de Sitter Space

    L. Susskind and E. Witten. “The Holographic Bound in Anti-de Sitter Space”,Preprint (1998) [arXiv:hep-th/9805114]

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  60. [61]

    Constraints on symmetry from holography

    D. Harlow and H. Ooguri. “Constraints on Symmetries from Holography”,Physical Review Letters122(2019) [arXiv:1810.05337]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  61. [62]

    Gauge Theory Correlators from Non-Critical String Theory

    S. Gubser, I. Klebanov and A. Polyakov. “Gauge theory correlators from non-critical string theory”,Physics Letters B428(1998) 105–114 [arXiv:hep-th/9802109]

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  62. [63]

    Mukhametzhanov, Large p SYK from chord diagrams , JHEP 09 (2023) 154 [2303.03474]

    B. Mukhametzhanov. “Large p SYK from chord diagrams”,Journal of High Energy Physics 2023(2023) [arXiv:2303.03474]

    work page arXiv 2023

  63. [64]

    Berkooz and O

    M. Berkooz and O. Mamroud. “A cordial introduction to double scaled SYK”,Reports on Progress in Physics88(2025) 036001 [arXiv:2407.09396]

    work page arXiv 2025

  64. [65]

    Lin and D

    H.W. Lin and D. Stanford. “A symmetry algebra in double-scaled SYK”,SciPost Phys.15 (2023) 234 [arXiv:2307.15725]

    work page arXiv 2023

  65. [66]

    Factoriality of Bozejko-Speicher von Neumann algebras

    P. ´Sniady. “Factoriality of Boejko–Speicher von Neumann Algebras”,Communications in Mathematical Physics246(2004) 561 [arXiv:math/0307201]

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  66. [67]

    Factoriality of q-Gaussian von Neumann algebras

    ´E. Ricard. “Factoriality of q-Gaussian von Neumann Algebras”,Communications in Mathematical Physics257(2005) 659 [arXiv:math/0311413]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  67. [68]

    The bulk Hilbert space of double scaled SYK,

    H.W. Lin. “The bulk Hilbert space of double-scaled SYK”,Journal of High Energy Physics 2022(2022) [arXiv:2208.07032]

    work page arXiv 2022

  68. [69]

    Von Neumann Algebras in Double-Scaled SYK

    J. Xu. “Von Neumann Algebras in Double-Scaled SYK”,Preprint(2025) [arXiv:2403.09021]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  69. [70]

    The operator algebra approach to quantum groups

    J. Kustermans and S. Vaes. “The operator algebra approach to quantum groups”, Proceedings of the National Academy of Sciences97(2000) 547

    work page 2000

  70. [71]

    Locally compact quantum groups

    J. Kustermans and S. Vaes. “Locally compact quantum groups”,Annales scientifiques de l’ ´Ecole Normale Sup´ erieure33(2000) 837

    work page 2000

  71. [72]

    G´ eom´ etrie non commutative

    A. Connes. “G´ eom´ etrie non commutative”. InterEditions Paris (1990)

    work page 1990

  72. [73]

    de Groot, M

    J. de Groot, M. Isachenkov and H. Posthuma. Work in Progress

    work page

  73. [74]

    A Pseudo-Riemannian Spectral Triple for SU(1,1)

    J. de Groot. “A Pseudo-Riemannian Spectral Triple for SU(1,1)”. To Appear

    work page

  74. [75]

    Unbounded elements affiliated with C*-algebras and non-compact quantum groups

    S.L. Woronowicz. “Unbounded elements affiliated with C*-algebras and non-compact quantum groups”,Communications in Mathematical Physics136(1991) 399

    work page 1991

  75. [76]

    Quantum groupSU(1,1)⋊Z 2 and “super-tensor

    L.I. Korogodsky. “Quantum groupSU(1,1)⋊Z 2 and “super-tensor” products”, Communications in Mathematical Physics163(1994) 433

    work page 1994

  76. [77]

    A locally compact quantum group analogue of the normalizer of SU(1,1) in SL(2,C)

    E. Koelink and J. Kustermans. “A Locally Compact Quantum Group Analogue of the Normalizer ofSU(1,1) inSL(2,C)”,Communications in Mathematical Physics233(2003) 231 [arXiv:math/0105117]. – 84 –

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  77. [78]

    The dual quantum group for the quantum group analogue of the normalizer of SU(1,1) in SL(2,C)

    W. Groenevelt, E. Koelink and J. Kustermans. “The Dual Quantum Group for the Quantum Group Analog of the Normalizer ofSU(1,1) inSL(2,C)”,International Mathematics Research Notices2010(2009) 1167 [arXiv:0905.2830]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  78. [79]

    Representation Theory of Semisimple Groups: An Overview Based on Examples

    A. Knapp. “Representation Theory of Semisimple Groups: An Overview Based on Examples”. Princeton University Press (1986)

    work page 1986

  79. [80]

    Representation of Lie Groups and Special Functions

    N.J. Vilenkin and A.U. Klimyk. “Representation of Lie Groups and Special Functions”. Mathematics and its Applications. Springer Dordrecht (1991)

    work page 1991

  80. [81]

    S. Lang. “SL2(R)”. Graduate Texts in Mathematics. Springer New York, NY (1985)

    work page 1985

Showing first 80 references.