Semisimple Hopf actions on Weyl algebras
We study actions of semisimple Hopf algebras H on Weyl algebras A over an algebraically closed field of characteristic zero. We show that the action of H on A must factor through a group action; in other words, if H acts inner faithfully on A, then H is cocommutative. The techniques used include red...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Elsevier
2017
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| Online Access: | http://hdl.handle.net/1721.1/111128 https://orcid.org/0000-0002-0710-1416 |
| _version_ | 1826197923409428480 |
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| author | Cuadra, Juan Etingof, Pavel I Walton, Chelsea |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Cuadra, Juan Etingof, Pavel I Walton, Chelsea |
| author_sort | Cuadra, Juan |
| collection | MIT |
| description | We study actions of semisimple Hopf algebras H on Weyl algebras A over an algebraically closed field of characteristic zero. We show that the action of H on A must factor through a group action; in other words, if H acts inner faithfully on A, then H is cocommutative. The techniques used include reduction modulo a prime number and the study of semisimple cosemisimple Hopf actions on division algebras. |
| first_indexed | 2024-09-23T10:55:52Z |
| format | Article |
| id | mit-1721.1/111128 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:55:52Z |
| publishDate | 2017 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | mit-1721.1/1111282022-10-01T00:02:41Z Semisimple Hopf actions on Weyl algebras Cuadra, Juan Etingof, Pavel I Walton, Chelsea Massachusetts Institute of Technology. Department of Mathematics Etingof, Pavel I Walton, Chelsea We study actions of semisimple Hopf algebras H on Weyl algebras A over an algebraically closed field of characteristic zero. We show that the action of H on A must factor through a group action; in other words, if H acts inner faithfully on A, then H is cocommutative. The techniques used include reduction modulo a prime number and the study of semisimple cosemisimple Hopf actions on division algebras. National Science Foundation (U.S.) (Grant DMS-1000113) National Science Foundation (U.S.) (Grant DMS-1401207) 2017-09-05T17:57:10Z 2017-09-05T17:57:10Z 2015-06 2015-03 Article http://purl.org/eprint/type/JournalArticle 0001-8708 1090-2082 http://hdl.handle.net/1721.1/111128 Cuadra, Juan et al. “Semisimple Hopf Actions on Weyl Algebras.” Advances in Mathematics 282 (September 2015): 47–55 © 2015 Elsevier Inc https://orcid.org/0000-0002-0710-1416 en_US http://dx.doi.org/10.1016/j.aim.2015.05.014 Advances in Mathematics Creative Commons Attribution-NonCommercial-NoDerivs License http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Elsevier arXiv |
| spellingShingle | Cuadra, Juan Etingof, Pavel I Walton, Chelsea Semisimple Hopf actions on Weyl algebras |
| title | Semisimple Hopf actions on Weyl algebras |
| title_full | Semisimple Hopf actions on Weyl algebras |
| title_fullStr | Semisimple Hopf actions on Weyl algebras |
| title_full_unstemmed | Semisimple Hopf actions on Weyl algebras |
| title_short | Semisimple Hopf actions on Weyl algebras |
| title_sort | semisimple hopf actions on weyl algebras |
| url | http://hdl.handle.net/1721.1/111128 https://orcid.org/0000-0002-0710-1416 |
| work_keys_str_mv | AT cuadrajuan semisimplehopfactionsonweylalgebras AT etingofpaveli semisimplehopfactionsonweylalgebras AT waltonchelsea semisimplehopfactionsonweylalgebras |