Twisting of Graded Quantum Groups and Solutions to the Quantum Yang-Baxter Equation
Abstract Let H be a Hopf algebra that is ℤ $\mathbb Z$ -graded as an algebra. We provide sufficient conditions for a 2-cocycle twist of H to be a Zhang twist o...
| Main Authors: | , , , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer US
2022
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| Online Access: | https://hdl.handle.net/1721.1/146745 |
| _version_ | 1811088040192376832 |
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| author | Huang, Hongdi Nguyen, Van C. Ure, Charlotte Vashaw, Kent B. Veerapen, Padmini Wang, Xingting |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Huang, Hongdi Nguyen, Van C. Ure, Charlotte Vashaw, Kent B. Veerapen, Padmini Wang, Xingting |
| author_sort | Huang, Hongdi |
| collection | MIT |
| description | Abstract
Let H be a Hopf algebra that is
ℤ
$\mathbb Z$
-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. |
| first_indexed | 2024-09-23T13:55:19Z |
| format | Article |
| id | mit-1721.1/146745 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T13:55:19Z |
| publishDate | 2022 |
| publisher | Springer US |
| record_format | dspace |
| spelling | mit-1721.1/1467452023-09-01T18:22:57Z Twisting of Graded Quantum Groups and Solutions to the Quantum Yang-Baxter Equation Huang, Hongdi Nguyen, Van C. Ure, Charlotte Vashaw, Kent B. Veerapen, Padmini Wang, Xingting Massachusetts Institute of Technology. Department of Mathematics Abstract Let H be a Hopf algebra that is ℤ $\mathbb Z$ -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. 2022-12-05T15:25:35Z 2022-12-05T15:25:35Z 2022-12-01 2022-12-04T04:11:34Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/146745 Huang, Hongdi, Nguyen, Van C., Ure, Charlotte, Vashaw, Kent B., Veerapen, Padmini et al. 2022. "Twisting of Graded Quantum Groups and Solutions to the Quantum Yang-Baxter Equation." PUBLISHER_CC en https://doi.org/10.1007/s00031-022-09779-9 Creative Commons Attribution https://creativecommons.org/licenses/by/4.0/ The Author(s) application/pdf Springer US Springer US |
| spellingShingle | Huang, Hongdi Nguyen, Van C. Ure, Charlotte Vashaw, Kent B. Veerapen, Padmini Wang, Xingting Twisting of Graded Quantum Groups and Solutions to the Quantum Yang-Baxter Equation |
| title | Twisting of Graded Quantum Groups and Solutions to the Quantum Yang-Baxter Equation |
| title_full | Twisting of Graded Quantum Groups and Solutions to the Quantum Yang-Baxter Equation |
| title_fullStr | Twisting of Graded Quantum Groups and Solutions to the Quantum Yang-Baxter Equation |
| title_full_unstemmed | Twisting of Graded Quantum Groups and Solutions to the Quantum Yang-Baxter Equation |
| title_short | Twisting of Graded Quantum Groups and Solutions to the Quantum Yang-Baxter Equation |
| title_sort | twisting of graded quantum groups and solutions to the quantum yang baxter equation |
| url | https://hdl.handle.net/1721.1/146745 |
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