POINTED HOPF ACTIONS ON CENTRAL SIMPLE DIVISION ALGEBRAS
Abstract We examine actions of finite-dimensional pointed Hopf algebras on central simple division algebras in characteristic 0. (By a Hopf action we mean a Hopf module algebra structure.) In all examples considered, we show that the given Hopf algebra does admit a faithful action on...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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Springer US
2022
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| Online Access: | https://hdl.handle.net/1721.1/142855 |
| _version_ | 1826196475870183424 |
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| author | ETINGOF, P. NEGRON, C. |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics ETINGOF, P. NEGRON, C. |
| author_sort | ETINGOF, P. |
| collection | MIT |
| description | Abstract
We examine actions of finite-dimensional pointed Hopf algebras on central simple division algebras in characteristic 0. (By a Hopf action we mean a Hopf module algebra structure.) In all examples considered, we show that the given Hopf algebra does admit a faithful action on a central simple division algebra, and we construct such a division algebra. This is in contrast to earlier work of Etingof and Walton, in which it was shown that most pointed Hopf algebras do not admit faithful actions on fields. We consider all bosonizations of Nichols algebras of finite Cartan type, small quantum groups, generalized Taft algebras with non-nilpotent skew primitive generators, and an example of non-Cartan type. |
| first_indexed | 2024-09-23T10:27:33Z |
| format | Article |
| id | mit-1721.1/142855 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T10:27:33Z |
| publishDate | 2022 |
| publisher | Springer US |
| record_format | dspace |
| spelling | mit-1721.1/1428552023-03-28T15:34:36Z POINTED HOPF ACTIONS ON CENTRAL SIMPLE DIVISION ALGEBRAS ETINGOF, P. NEGRON, C. Massachusetts Institute of Technology. Department of Mathematics Abstract We examine actions of finite-dimensional pointed Hopf algebras on central simple division algebras in characteristic 0. (By a Hopf action we mean a Hopf module algebra structure.) In all examples considered, we show that the given Hopf algebra does admit a faithful action on a central simple division algebra, and we construct such a division algebra. This is in contrast to earlier work of Etingof and Walton, in which it was shown that most pointed Hopf algebras do not admit faithful actions on fields. We consider all bosonizations of Nichols algebras of finite Cartan type, small quantum groups, generalized Taft algebras with non-nilpotent skew primitive generators, and an example of non-Cartan type. 2022-05-31T19:51:25Z 2022-05-31T19:51:25Z 2022-01-03 2022-05-31T03:22:23Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/142855 ETINGOF, P. and NEGRON, C. 2022. "POINTED HOPF ACTIONS ON CENTRAL SIMPLE DIVISION ALGEBRAS." en https://doi.org/10.1007/s00031-021-09690-9 Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International https://creativecommons.org/licenses/by-nc-sa/4.0/ The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature application/pdf Springer US Springer US |
| spellingShingle | ETINGOF, P. NEGRON, C. POINTED HOPF ACTIONS ON CENTRAL SIMPLE DIVISION ALGEBRAS |
| title | POINTED HOPF ACTIONS ON CENTRAL SIMPLE DIVISION ALGEBRAS |
| title_full | POINTED HOPF ACTIONS ON CENTRAL SIMPLE DIVISION ALGEBRAS |
| title_fullStr | POINTED HOPF ACTIONS ON CENTRAL SIMPLE DIVISION ALGEBRAS |
| title_full_unstemmed | POINTED HOPF ACTIONS ON CENTRAL SIMPLE DIVISION ALGEBRAS |
| title_short | POINTED HOPF ACTIONS ON CENTRAL SIMPLE DIVISION ALGEBRAS |
| title_sort | pointed hopf actions on central simple division algebras |
| url | https://hdl.handle.net/1721.1/142855 |
| work_keys_str_mv | AT etingofp pointedhopfactionsoncentralsimpledivisionalgebras AT negronc pointedhopfactionsoncentralsimpledivisionalgebras |