分级量子群的扭曲与量子Yang-Baxter方程的解

IF 0.4 3区数学 Q4 MATHEMATICS

Transformation Groups Pub Date : 2024-01-01 Epub Date: 2022-12-01 DOI:10.1007/s00031-022-09779-9

Hongdi Huang, Van C Nguyen, Charlotte Ure, Kent B Vashaw, Padmini Veerapen, Xingting Wang

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引用次数: 0

摘要

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Twisting of Graded Quantum Groups and Solutions to the Quantum Yang-Baxter Equation.

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Twisting of Graded Quantum Groups and Solutions to the Quantum Yang-Baxter Equation.

Let H be a Hopf algebra that is $ℤ$ -graded as an algebra. We provide sufficient conditions for a 2-cocycle twist of H to be a Zhang twist of H. In particular, we introduce the notion of a twisting pair for H such that the Zhang twist of H by such a pair is a 2-cocycle twist. We use twisting pairs to describe twists of Manin's universal quantum groups associated with quadratic algebras and provide twisting of solutions to the quantum Yang-Baxter equation via the Faddeev-Reshetikhin-Takhtajan construction.

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来源期刊

Transformation Groups 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

100

审稿时长

9 months

期刊介绍： Transformation Groups will only accept research articles containing new results, complete Proofs, and an abstract. Topics include: Lie groups and Lie algebras; Lie transformation groups and holomorphic transformation groups; Algebraic groups; Invariant theory; Geometry and topology of homogeneous spaces; Discrete subgroups of Lie groups; Quantum groups and enveloping algebras; Group aspects of conformal field theory; Kac-Moody groups and algebras; Lie supergroups and superalgebras.