Extended jordanian twists for Lie algebras

A.I. Mudrov; P.P. Kulish; V.D. Lyakhovsky

RECORD

Extended jordanian twists for Lie algebras

P.P. Kulish, V.D. Lyakhovsky, A.I. Mudrov

Quantum Algebra · Submitted 3 Jun 1998

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim It is shown that the twisted Hopf algebra ${\cal U}_{\cal F} ({\bf B}^{\vee})$ is self dual.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,309 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.13 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.59 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

Jordanian quantizations of Lie algebras are studied using the factorizable twists. For a restricted Borel subalgebras ${\bf B}^{\vee}$ of $sl(N)$ the explicit expressions are obtained for the twist element ${\cal F}$, universal ${\cal R}$-matrix and the corresponding canonical element ${\cal T}$. It is shown that the twisted Hopf algebra ${\cal U}_{\cal F} ({\bf B}^{\vee})$ is self dual. The cohomological properties of the involved Lie bialgebras are studied to justify the existence of a contraction from the Dinfeld-Jimbo quantization to the jordanian one. The construction of the twist is generalized to a certain type of inhomogenious Lie algebras.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Jordanian quantizations of Lie algebras are studied using the factorizable twists.	contribution 0.66	0.70	0.09	asserted 0.97
s1	For a restricted Borel subalgebras ${\bf B}^{\vee}$ of $sl(N)$ the explicit expressions are obtained for the twist element ${\cal F}$, universal ${\cal R}$-matrix and the corresponding canonical element ${\cal T}$.	result 0.87	0.93	0.15	asserted 1.00
s2	It is shown that the twisted Hopf algebra ${\cal U}_{\cal F} ({\bf B}^{\vee})$ is self dual.	result 1.00	0.91	0.27	asserted 1.00
s3	The cohomological properties of the involved Lie bialgebras are studied to justify the existence of a contraction from the Dinfeld-Jimbo quantization to the jordanian one.	contribution 0.56	0.85	0.12	asserted 1.00
s4	The construction of the twist is generalized to a certain type of inhomogenious Lie algebras.	contribution 0.95	0.89	0.12	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

Jordanian quantizations of Lie algebras are studied using the factorizable twists. For a restricted Borel subalgebras ${\bf B}^{\vee}$ of $sl(N)$ the explicit expressions are obtained for the twist element ${\cal F}$, universal ${\cal R}$-matrix and the corresponding canonical element ${\cal T}$. It is shown that the twisted Hopf algebra ${\cal U}_{\cal F} ({\bf B}^{\vee})$ is self dual. The cohomological properties of the involved Lie bialgebras are studied to justify the existence of a contraction from the Dinfeld-Jimbo quantization to the jordanian one. The construction of the twist is generalized to a certain type of inhomogenious Lie algebras.

Human review

How Pith checks papers → · Full audit of this paper →

References

Forward citations

Cited by 4 Pith papers

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

Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory
hep-th 2015-06 conditional novelty 7.0 of 10

Homogeneous Yang-Baxter deformations of the AdS5 x S5 string are Drinfeld twists of the symmetry algebra, and their gauge duals are conjectured to be twist-noncommutative N=4 SYM, with brane-construction support for t...
Homogeneous Yang-Baxter deformations as non-abelian duals of the AdS_5 sigma-model
hep-th 2016-09 conditional novelty 6.0 of 10

Homogeneous Yang-Baxter deformations of the AdS5 sigma-model are shown, example by example, to coincide with non-abelian duals of the undeformed model with respect to subgroups read off from the r-matrix.
Jordanian deformations of the AdS_5xS^5 superstring
hep-th 2014-01 conditional novelty 6.0 of 10

Twisting the q-deformed AdS5 x S5 superstring with Jordanian R operators yields a new class of integrable deformations whose action preserves kappa-symmetry, including partial deformations of only the S5 part.
Lunin-Maldacena backgrounds from the classical Yang-Baxter equation -- Towards the gravity/CYBE correspondence
hep-th 2014-04 accept novelty 5.0 of 10

Abelian classical r-matrices satisfying the Yang-Baxter equation reproduce the Lunin-Maldacena gamma-deformed AdS5xS5 background, linking TsT transformations to abelian twists.

How the literature uses it

13 arXiv papers cite this in 17 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 13 sentences without a confident label

Builds on it 1 paper

We deform the conformal Hopf algebra $U(𝔠)$ ([ref], [ref], [ref], [ref]) with the twist $ℱ_LL$ leading to light-like $κ$-deformation of Poincaré algebra [ref] (which is related to extended Jordanian twist [ref] , [ref] )[The explicit relation between the twist ([ref]) and the standard extended Jordanian twist corresponding to light-like case (up to the transposition) is presented in detail in sect.

Twisted conformal algebra related to $\kappa$-Minkowski space · Light-like $κ-$deformation of Poincaré algebra extended to the conformal algebra · 0.88

Cites it as background 3 papers

In the light-cone basis, the $κ$-Poincaré algebra was studied in [ref] and [ref] , the corresponding twist is extended Jordanian twist, written in terms of two exponential factors.

Realizations of $\kappa$-Minkowski space, Drinfeld twists and related symmetry algebras · Light-cone deformation · 0.87
To understand $κ$-MST more deeply, twist formalism such as Jordanian twist [ref] , $κ$-like deformation of quantum Weyl and conformal algebra [ref] and the light-cone $κ$-deformation of Poincaré algebra [ref] has been tried.

Braided Statistics from Abelian Twist in $\kappa$-Minkowski Spacetime · Introduction · 0.85
One may also consider the chains of twists for classical Lie algebras [ref] .

Differential Structure on kappa-Minkowski Spacetime Realized as Module of Twisted Weyl Algebra · Introduction · 0.93

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.