Pith. sign in

REVIEW 1 minor 1 cited by

The paper expands the list of open problems and conjectures in axial algebras beyond a recent survey.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · grok-4.3

2026-06-30 03:28 UTC pith:7LQGKDXN

load-bearing objection This is a curated list of open problems in axial algebras that expands an existing survey, with no new theorems or proofs.

arxiv 2606.30048 v1 pith:7LQGKDXN submitted 2026-06-29 math.RA

Axial Algebras: Questions and Conjectures

I. Gorshkov , S. Shpectorov This is my paper
classification math.RA
keywords axial algebrasopen problemsconjecturesfusion lawsnon-associative algebrasidempotentsautomorphisms
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Axial algebras are non-associative algebras generated by idempotents called axes whose adjoint actions satisfy a fusion law. When the fusion law is graded, the axes produce automorphisms that link the algebras to groups. This article complements an earlier survey by significantly expanding the list of interesting open problems suggested by specialists. It also supplies further discussion of related concepts and available results. A reader would care because the problems point to concrete directions for work in non-associative algebra and its ties to group theory.

Core claim

The authors significantly expand the list of interesting open problems in axial algebras and provide further discussion of related concepts and available results, complementing the recent survey.

What carries the argument

Axial algebra: non-associative algebra generated by idempotents (axes) whose adjoint action satisfies a fusion law, often yielding group automorphisms when the law is graded.

Load-bearing premise

The listed problems are genuinely open, significant to specialists, and accurately described relative to the prior survey.

What would settle it

A check showing that several listed problems have already been resolved in the literature would falsify the claim that the paper expands the set of open problems.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

0 major / 1 minor

Summary. The manuscript is a curated collection of open questions and conjectures in the theory of axial algebras. It complements the recent survey [ms] by expanding the list of interesting open problems suggested by specialists and providing further discussion of related concepts and available results. Axial algebras are defined as non-associative algebras generated by idempotents (axes) whose adjoint actions satisfy a fusion law; when graded, these induce automorphisms linking the algebras to groups.

Significance. This work provides a service to the axial algebra community by systematically expanding the catalog of open problems. If the listed items are accurately described as open and of interest to specialists, the manuscript can help direct future research in non-associative algebras and their connections to finite groups. No new theorems, proofs, or computational results are claimed, so the contribution rests on the utility of the curated list rather than on technical derivations.

minor comments (1)
  1. The abstract and introduction reference the survey as [ms] without a full bibliographic entry visible in the provided text; ensure the reference list includes the complete citation for [ms] to allow readers to locate the prior survey.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive evaluation of the manuscript and for recommending acceptance. The report accurately captures the purpose of the work as a curated expansion of open questions to complement the recent survey.

Circularity Check

0 steps flagged

No circularity; paper is a curated list of open questions with no derivations

full rationale

The manuscript contains no theorems, proofs, equations, predictions, or fitted parameters. Its sole purpose is to expand a list of open problems complementing the cited survey [ms]. All references to prior work serve only to frame questions and are not load-bearing for any internal claim. No self-citation reduces a result to an unverified input, and the paper is self-contained as a non-technical survey of open items.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No free parameters, axioms, or invented entities are introduced because the paper contains no derivations or new constructions; it only lists questions about existing concepts.

pith-pipeline@v0.9.1-grok · 5599 in / 951 out tokens · 55132 ms · 2026-06-30T03:28:47.399338+00:00 · methodology

0 comments
Cite this review

Pith. "Pith review of Axial Algebras: Questions and Conjectures." pith.science (2026). https://pith.science/paper/7LQGKDXN

@misc{pith2026260630048,
  author       = {Pith},
  title        = {Pith review of: Axial Algebras: Questions and Conjectures},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7LQGKDXN}},
  note         = {Machine review of arXiv:2606.30048}
}
Share X Bluesky LinkedIn Reddit HN
read the original abstract

Axial algebras are non-associative algebras generated by idempotents, called axes, whose adjoint action satisfies a fusion law. When this fusion law is graded, axes naturally lead to automorphisms of the algebra, and so such axial algebras are inextricably linked with groups. This article is meant to complement the recent survey \cite{ms} by significantly expanding the list of interesting open problems suggested by the specialists in the field, and providing a further discussion of the related concepts and available results.

Figures

Figures reproduced from arXiv: 2606.30048 by I. Gorshkov, S. Shpectorov.

Figure 1
Figure 1. Figure 1: Monster fusion law This table represents what is now called a fusion law, specifically, the Monster fusion law, and it describes the properties of the adjoint action of Majorana axes. Up to our knowledge, this was the first time a fusion law appeared as part of the axiomatics of a class of algebras. However, similar properties of idempotents in algebras have been observed earlier. In 1881, Peirce [P] descr… view at source ↗
Figure 2
Figure 2. Figure 2: Associative fusion law In 1947, Albert introduced three-term Peirce decompositions in Jordan algebras. Again, these are with respect to an arbitrary idempotent and they can be described by [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Jordan fusion law 2 Background This section introduces the foundational definitions of axial algebras and their subclasses, focusing on algebras of Jordan and Monster type. Definition 2.1 A fusion law is a pair (F, ∗), where F is a set and ∗ : F × F → 2 F is a binary operation on F with values in the set 2 F of all subsets of F. The fusion laws we focus on are defined on a small set F, and we find it usefu… view at source ↗
Figure 4
Figure 4. Figure 4: shows the fusion law of Jordan type η, denoted by J (η). Here F = J (η) = {1, 0, η}, η ̸= 1, 0, is a subset of a field F. The fusion law J (η) generalises the Jordan fusion law from [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Monster type fusion law M(α, β) (b) For λ ∈ F, set Aλ(a) = {b ∈ A|ada(b) = λb} = {b ∈ A|ab = λb}. (c) For Λ ⊆ F, set AΛ(a) = L λ∈Λ Aλ(a). Let F ⊆ F be a fusion law. Definition 2.3 An idempotent 0 ̸= a ∈ A is an F-axis if (a) A = AF (a); and (b) Aλ(a)Aµ(a) ⊆ Aλ∗µ(a) for all λ, µ ∈ F. If it is clear which fusion law we are considering, we will simply call a an axis. This definition assumes that 1 ∈ F, as ada… view at source ↗
Figure 6
Figure 6. Figure 6: Fusion law M(4η, 4η) This product also works in the group 52 : 2, but not in A5 if for products of order 1, 2, and 3 the usual Matsuo multiplication is used. 6.2 Almost Jordan type fusion law Whybrow [W] did an algorithmic study of all fusion laws of small size. In particular, she observed that for the almost Jordan type fusion law, shown in [PITH_FULL_IMAGE:figures/full_fig_p033_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Fusion law J (α, β) type. algebras can be classified. This was developed further by Afanasev [Af], who provided a nearly complete classification of 2-generated primitive algebras of almost Jordan type (α, β). More recently, Welch [SW] completed Afanasiev’s classification and he also developed some non 2-generated examples for this fusion law, including generalised Matsuo algebras for 3- transposition group… view at source ↗
Figure 8
Figure 8. Figure 8: The fusion law F for Hˆ 5, the eigenvalue 5 2 becomes zero, and the fusion law folds into the Monster type (2, 1 2 ) fusion law. Problem 6.6 Is it possible to classify primitive algebras with the above extended Monster type fusion law. C. Franchi, M. Mainardis 6.4 Axial algebras from graphs and geometries Cuypers [Cu] developed a very interesting construction building axial algebras with fusion laws simila… view at source ↗
Figure 9
Figure 9. Figure 9: Fusion law H for Hsiang algebras 35 [PITH_FULL_IMAGE:figures/full_fig_p035_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Fusion law B for type Bn. This is a C2-graded fusion law with the partition F+ = {1, 0} and F− = { 1 2 , 1 4 }. Problem 6.12 Is it possible to classify 2-generated primitive axial algebras with the fusion law B? S. Shpectorov If this first step is doable then the much more ambitious question would be the following. Problem 6.13 Are the Chayet-Garibaldi algebras of type Bn characterised by the fusion law B… view at source ↗
Figure 11
Figure 11. Figure 11: Fusion law CG for type Cn, F4. More generally, all Chayet-Garibaldi algebras, except the one arising for the type G2, have primitive idempotents obeying the fusion law in [PITH_FULL_IMAGE:figures/full_fig_p037_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Fusion law G for type G2. We will formulate the following blanket questions concerning these fusion laws. Problem 6.14 What can we say about algebras with fusion laws CG and G? E.g., can 2-generated primitive algebras with these fusion laws be classified? S. Shpectorov Note that the fusion law CG is amazingly close to the Monster fusion law M( 1 4 , 1 32 ). Namely, the Monster fusion law is a sub fusion l… view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Fusion rules from the Norton inequality

    math.RA 2026-07 accept novelty 6.5

    Norton inequality forces A0(e) and A1(e) to be subalgebras and A0(e)A1(e)subseteq A1/2(e) for non-degenerate Frobenius forms; a degenerate counter-example is given.

Reference graph

Works this paper leans on

76 extracted references · 9 canonical work pages · cited by 1 Pith paper · 1 internal anchor

  1. [1]

    Alharbi, Automorphism groups of Matsuo algebras , Ph.D

    F. Alharbi, Automorphism groups of Matsuo algebras , Ph.D. thesis, University of Birmingham (2024)

    2024

  2. [2]

    Alsaeedi, V

    M. Alsaeedi, V. Bovdi, S. Shpectorov, Flip subalgebras in Matsuo algebras for extended symmetric groups , in preparation

  3. [3]

    Afanasev, On axial algebras with 3 eigenvalues , arXiv:2410.02034

    V. Afanasev, On axial algebras with 3 eigenvalues , arXiv:2410.02034

    work page arXiv

  4. [4]

    Bergman, A note on growth functions of algebras and semigroups , mimeographed notes, University of California, Berkeley (1978)

    G.M. Bergman, A note on growth functions of algebras and semigroups , mimeographed notes, University of California, Berkeley (1978)

    1978

  5. [5]

    Bildanov, I

    R. Bildanov, I. Gorshkov, On 3-generated axial algebras of Jordan type 1 2 , Commun. Math. 33 :3 (2025), Paper No. 4, 12 p

    2025

  6. [6]

    Buekenhout, La géometrie des groupes de Fischer , preprint, Univ

    F. Buekenhout, La géometrie des groupes de Fischer , preprint, Univ. Libre de Bruxelles

  7. [7]

    Cantarini, V

    N. Cantarini, V. Kac, Classification of linearly compact simple rigid superalgebras , Int. Math. Res. Not. IMRN, 17 (2010), 3341--3393

    2010

  8. [8]

    Cuypers, Graphs, axial algebras and their automorphism groups , arXiv:2603.03822

    H. Cuypers, Graphs, axial algebras and their automorphism groups , arXiv:2603.03822

    work page arXiv

  9. [9]

    Cuypers, J.I

    H. Cuypers, J.I. Hall, The 3-transposition groups with trivial center , J. Algebra 178 (1995), 149--193

    1995

  10. [10]

    Centrone, Private communication

    L. Centrone, Private communication

  11. [11]

    Chayet, S

    M. Chayet, S. Garibaldi. A class of continuous non-associative algebras arising from algebraic groups including E_8 , Forum Math. Sigma 9 (2021)

    2021

  12. [12]

    Conway, A simple construction for the Fischer-Griess monster group , Invent

    J.H. Conway, A simple construction for the Fischer-Griess monster group , Invent. Math., 79 (1985), 513--540

    1985

  13. [13]

    De Medts, F

    T. De Medts, F. Rehren, Jordan algebras and 3 -transposition groups , J. Algebra 478 , (2017) 318--340

    2017

  14. [14]

    De Medts, L

    T. De Medts, L. Rowen, Y. Segev, Primitive 4 -generated axial algebras of Jordan type , Proc. Am. Math. Soc. 152 :2 (2024), 537--551

    2024

  15. [15]

    De Medts, M

    T. De Medts, M. Van Couwenberghe, Modules over axial algebras , Algebr. Represent. Theory 23 :1 (2020), 209--227

    2020

  16. [16]

    Desmet, Non-associative aspects of algebraic groups , PhD thesis, University of Ghent, 2025

    J. Desmet, Non-associative aspects of algebraic groups , PhD thesis, University of Ghent, 2025

    2025

  17. [17]

    Desmet, Solid lines in axial algebras of Jordan-type 1 2 and Jordan algebras , Proc

    J. Desmet, Solid lines in axial algebras of Jordan-type 1 2 and Jordan algebras , Proc. Am. Math. Soc. 153 :4 (2025), 1461--1479

    2025

  18. [18]

    Desmet, Automorphism groups of Matsuo algebras , arXiv:2511.10084

    J. Desmet, Automorphism groups of Matsuo algebras , arXiv:2511.10084

    work page arXiv

  19. [19]

    Desmet, In preparation

    J. Desmet, In preparation

  20. [20]

    Desmet, S

    J. Desmet, S. Shpectorov, Components in algebras of Jordan type half , in preparation

  21. [21]

    Etherington, Genetic algebras , Proc

    I.M.H. Etherington, Genetic algebras , Proc. Roy. Soc. Edinburgh, 59 (1939), 242--258

    1939

  22. [22]

    Fischer, Distributive Quasigruppen endlicher Ordnung , Mathematische Zeitschrift, 83 :4 (1964), 267--303

    B. Fischer, Distributive Quasigruppen endlicher Ordnung , Mathematische Zeitschrift, 83 :4 (1964), 267--303

    1964

  23. [23]

    Fischer, Finite groups generated by 3-transpositions , I

    B. Fischer, Finite groups generated by 3-transpositions , I. Invent. Math. 13 (1971), 232-246

    1971

  24. [24]

    Franchi, A

    C. Franchi, A. Ivanov, M. Mainardis, Saturated Majorana representations of A_ 12 , Trans. Am. Math. Soc, 375 :8 (2022), 5753--5801

    2022

  25. [25]

    Franchi, A

    C. Franchi, A. Ivanov, M. Mainardis, Standard Majorana representations of the symmetric groups , J. Algebr. Comb. 44 :2 (2016), 265--292

    2016

  26. [26]

    Franchi, M

    C. Franchi, M. Mainardis, On subalgebras of the Griess algebra with alternating Miyamoto group , J. Algebra, 691 (2026), 811--854

    2026

  27. [27]

    Franchi, M

    C. Franchi, M. Mainardis, Classifying 2-generated symmetric axial algebras of Monster type , J. Algebra, 596 (2022), 200--218

    2022

  28. [28]

    Franchi, M

    C. Franchi, M. Mainardis, J. McInroy, Quotients of the Highwater algebra and its cover , J. Algebra 640 (2024), 432 -- 476

    2024

  29. [29]

    The Classification of the 2-generated Primitive Axial Algebras of Monster Type

    C. Franchi, M. Mainardis, J. McInroy, M. Turner, The Classification of the 2-generated Primitive Axial Algebras of Monster Type , arXiv:2605.18737

    work page internal anchor Pith review Pith/arXiv arXiv

  30. [30]

    Franchi, M

    C. Franchi, M. Mainardis, S. Shpectorov, An infinite-dimensional 2-generated primitive axial algebra of monster type , Ann. Mat. Pura Appl. 201 :4 (2022), 1279--1293

    2022

  31. [31]

    Franchi, M

    C. Franchi, M. Mainardis, S. Shpectorov, 2-generated axial algebras of Monster type (2 , ) , J. Algebra 636 (2023), 123--170

    2023

  32. [32]

    Franchi, M

    C. Franchi, M. Mainardis, S. Shpectorov, 2-generated axial algebras of Monster type , J. Algebra 683 (2025), 60--115

    2025

  33. [33]

    A. Galt, V. Joshi, A. Mamontov, S. Shpectorov, A. Staroletov, Double axes and subalgebras of monster type in Matsuo algebras , Commun. Algebra 49 :10 (2021), 4208--4248

    2021

  34. [34]

    The GAP Group, GAP – Groups, Algorithms, and Programming, Version 4.12.2; 2022, https://www.gap-system.org

    2022

  35. [35]

    Guterman, D.K

    A.E. Guterman, D.K. Kudryavtsev, Upper bounds for the length of non-associative algebras , J. Algebra 544 (2020), 483--497

    2020

  36. [36]

    Griess Jr., The friendly giant , Ivent

    R.L. Griess Jr., The friendly giant , Ivent. Math. 69 (1982), 1--102

    1982

  37. [37]

    Gorshkov, A

    I. Gorshkov, A. Mamontov, A. Staroletov, On Jordan algebras that are factors of Matsuo algebras , Int. Electron. J. Algebra 37 (2025), 70--90

    2025

  38. [38]

    Gorshkov, J

    I. Gorshkov, J. McInroy, T.M. Mudziiri Shumba, S. Shpectorov, Automorphism groups of axial algebras , J. Algebra 661 (2025), 657--712

    2025

  39. [39]

    Gorshkov, S

    I. Gorshkov, S. Shpectorov, A. Staroletov, Solid subalgebras in algebras of Jordan type half , arXiv:2401.16218

    work page arXiv

  40. [40]

    Gorshkov, A

    I. Gorshkov, A. Staroletov, On primitive 3-generated axial algebras of Jordan type , J. Algebra 563 (2020), 74--99

    2020

  41. [41]

    J.I. Hall, F. Rehren, S. Shpectorov, Universal Axial Algebras and a Theorem of Sakuma , J. Algebra 421 (2015), 394--424

    2015

  42. [42]

    J.I. Hall, F. Rehren, S. Shpectorov, Primitive axial algebras of Jordan type , J. Algebra 437 (2015), 379-–115

    2015

  43. [43]

    J.I. Hall, Y. Segev, S. Shpectorov, Miyamoto involutions in axial algebras of Jordan type half , Israel J. Math. 223 (2018), 261--308

    2018

  44. [44]

    J.I. Hall, Y. Segev, and S. Shpectorov, On primitive axial algebras of Jordan type , Bull. Inst. Math. Acad. Sin. (N.S.) 13 :4 (2018), 397--409

    2018

  45. [45]

    Ivanov, The Monster Group and Majorana Involutions , Cambridge Tracts in Mathematics 176, Cambridge University Press, 2009

    A.A. Ivanov, The Monster Group and Majorana Involutions , Cambridge Tracts in Mathematics 176, Cambridge University Press, 2009

    2009

  46. [46]

    Ivanov, D.V

    A.A. Ivanov, D.V. Pasechnik, A. Seress, S. Shpectorov, Majorana representations of the symmetric group of degree 4 , J. Algebra 324 :9 (2010) 2432--2463

    2010

  47. [47]

    Joshi, Axial algebras of Monster type (2 , ) , Ph.D

    V. Joshi, Axial algebras of Monster type (2 , ) , Ph.D. thesis, University of Birmingham (2020)

    2020

  48. [48]

    Kantor, Certain generalizations of Jordan algebras (Russian) , Trudy Sem

    I. Kantor, Certain generalizations of Jordan algebras (Russian) , Trudy Sem. Vektor. Tenzor. Anal., 16 (1972), 407--499

    1972

  49. [49]

    Kantor, Some problems in L-functor theory , Trudy Inst

    I. Kantor, Some problems in L-functor theory , Trudy Inst. Mat. (Novosibirsk), 16 (1989), Issled. po Teor. Kolets i Algebr, 54--75, 198

    1989

  50. [50]

    Kaygorodov, C

    I. Kaygorodov, C. Martín González, P. Páez-Guillán, Central extensions of axial algebras , J. Algebra 662 (2025), 797--831

    2025

  51. [51]

    Khasraw, J

    S.M.S. Khasraw, J. McInroy, S. Shpectorov, On the structure of axial algebras , Trans. Amer. Math. Soc. 373 :3 (2020), 2135--2156

    2020

  52. [52]

    Krause, T.H

    G. Krause, T.H. Lenagan, Growth of Algebras and Gelfand-Kirillov Dimension , Research Notes in Math. 116 (1985)

    1985

  53. [53]

    Computer algebra system (CAS)

    MAGMA. Computer algebra system (CAS). http://magma.maths.usyd.edu.au/magma/

  54. [54]

    Mamontov, S

    A. Mamontov, S. Shpectorov, V. Zhelyabin, Radicals in primitive axial algebras , arXiv:2602.11984

    work page arXiv

  55. [55]

    Mamontov, A

    A. Mamontov, A. Staroletov, Axial algebras of Monster type (2 , ) for D diagrams , Commun. Algebra 53 :8 (2025), 3218--3252

    2025

  56. [56]

    Martinez, E

    C. Martinez, E. Zelmanov, Jordan algebras of Gelfand-Kirillov dimension one , J. Algebra 180 :1 (1996), 211--238

    1996

  57. [57]

    McInroy, S

    J. McInroy, S. Shpectorov, An expansion algorithm for constructing axial algebras , J. Algebra, 550 (2020), 379--409

    2020

  58. [58]

    McInroy, S

    J. McInroy, S. Shpectorov, Axial algebras of Jordan and Monster type , London Math. Soc. Lecture Note Ser., 496 , Cambridge University Press, Cambridge (2025), 246--294

    2025

  59. [59]

    Miyamoto, Griess algebras and conformal vectors in vertex operator algebras , J

    M. Miyamoto, Griess algebras and conformal vectors in vertex operator algebras , J. Algebra 179 :2 (1996), 523--548

    1996

  60. [60]

    Miyamoto, Vertex operator algebras generated by two conformal vectors whose -involutions generate S_3 , J

    M. Miyamoto, Vertex operator algebras generated by two conformal vectors whose -involutions generate S_3 , J. Algebra 268 :2 (2003), 653--671

    2003

  61. [61]

    Osborn, Identities of non-associative algebras , Canad

    J.M. Osborn, Identities of non-associative algebras , Canad. J. Math. 19 :21 (1965), 78--92

    1965

  62. [62]

    Parker, M

    C. Parker, M. Turner, Almost simple and quasisimple groups of 6 -transpositions , in preparation

  63. [63]

    Peirce, Linear Associative Algebra , American Journal of Mathematics, 4 :1 (1881), 97--229

    B. Peirce, Linear Associative Algebra , American Journal of Mathematics, 4 :1 (1881), 97--229

  64. [64]

    Rehren, Axial algebras ,Ph.D

    F.G. Rehren, Axial algebras ,Ph.D. thesis, University of Birmingham, 2015

    2015

  65. [65]

    Rehren, Generalised dihedral subalgebras from the Monster , Trans

    F. Rehren, Generalised dihedral subalgebras from the Monster , Trans. Am. Math. Soc., 369 :10 (2017), 6953--6986

    2017

  66. [66]

    Rowen, AXIAL IDENTITIES, arXiv:2508.16427

    L. Rowen, AXIAL IDENTITIES, arXiv:2508.16427

    work page arXiv

  67. [67]

    Sakuma, 6-transposition property of -involutions of vertex operator algebras , Int

    S. Sakuma, 6-transposition property of -involutions of vertex operator algebras , Int. Math. Res. Not. IMRN 9 (2007), 19 p

    2007

  68. [68]

    R. D. Schafer, Inner derivations of non-associative algebras , Bull. Am. Math. Soc. 55 (1949), 769--776

    1949

  69. [69]

    Segev, Half-axes in power associative algebras , J

    Y. Segev, Half-axes in power associative algebras , J. Algebra 510 (2018), 1--23

    2018

  70. [70]

    Shpectorov, B

    S. Shpectorov, B. Welch, Classification of primitive 2 -generated axial algebras of type ( , ) , in preparation

  71. [71]

    Shi, Baric Axial Algebras of Jordan Type , Ph.D

    Y. Shi, Baric Axial Algebras of Jordan Type , Ph.D. thesis, University of Birmingham, 2025

    2025

  72. [72]

    Tkachev, The universality of one half in commutative nonassociative algebras with identities , J

    V.G. Tkachev, The universality of one half in commutative nonassociative algebras with identities , J. Algebra 569 (2021), 466--510

    2021

  73. [73]

    Turner, Skew axial algebras of Monster type , J

    M. Turner, Skew axial algebras of Monster type , J. Algebra 652 (2024), 67--93

    2024

  74. [74]

    Turner, Skew axial algebras of Monster type II , arXiv:2311.00520

    M. Turner, Skew axial algebras of Monster type II , arXiv:2311.00520

    work page arXiv

  75. [75]

    Yabe, On the classification of 2 -generated axial algebras of Majorana type , J

    T. Yabe, On the classification of 2 -generated axial algebras of Majorana type , J. Algebra, 619 (2023), 347--382

    2023

  76. [76]

    Whybrow, Graded 2-generated axial algebras , arXiv:2005.03577

    M. Whybrow, Graded 2-generated axial algebras , arXiv:2005.03577

    work page arXiv 2005