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

{"title":"分级量子群的扭曲与量子Yang-Baxter方程的解","authors":"Hongdi Huang, Van C Nguyen, Charlotte Ure, Kent B Vashaw, Padmini Veerapen, Xingting Wang","doi":"10.1007/s00031-022-09779-9","DOIUrl":null,"url":null,"abstract":"Let H be a Hopf algebra that is <math><mi>ℤ</mi></math> -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.","PeriodicalId":49423,"journal":{"name":"Transformation Groups","volume":" ","pages":"1459-1500"},"PeriodicalIF":0.4000,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11641468/pdf/","citationCount":"0","resultStr":"{\"title\":\"Twisting of Graded Quantum Groups and Solutions to the Quantum Yang-Baxter Equation.\",\"authors\":\"Hongdi Huang, Van C Nguyen, Charlotte Ure, Kent B Vashaw, Padmini Veerapen, Xingting Wang\",\"doi\":\"10.1007/s00031-022-09779-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let H be a Hopf algebra that is <math><mi>ℤ</mi></math> -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.\",\"PeriodicalId\":49423,\"journal\":{\"name\":\"Transformation Groups\",\"volume\":\" \",\"pages\":\"1459-1500\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2024-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11641468/pdf/\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transformation Groups\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00031-022-09779-9\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2022/12/1 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transformation Groups","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00031-022-09779-9","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2022/12/1 0:00:00","PubModel":"Epub","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要图片

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

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.

期刊最新文献

Stability of $$\imath $$ canonical Bases of Locally Finite Type Counting Parabolic Principal G-Bundles with Nilpotent Sections Over $$\mathbb {P}^{1}$$ Regularity of Unipotent Elements in Total Positivity Rational Singularities for Moment Maps of Totally Negative Quivers Filtered Fiber Functors Over a General Base