Classification of Linearly Compact Simple Rigid Superalgebras
The notion of an anti-commutative (resp. commutative) rigid superalgebra is a natural generalization of the notion of a Lie (resp. Jordan) superalgebra. Intuitively, rigidity means that small deformations of the product under the action of the structural group produce an isomorphic algebra. In this...
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| Format: | Article |
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Oxford University Press (OUP)
2018
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| Online Access: | http://hdl.handle.net/1721.1/115845 https://orcid.org/0000-0002-2860-7811 |
| _version_ | 1811087342052573184 |
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| author | Cantarini, N. Kac, Victor |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Cantarini, N. Kac, Victor |
| author_sort | Cantarini, N. |
| collection | MIT |
| description | The notion of an anti-commutative (resp. commutative) rigid superalgebra is a natural generalization of the notion of a Lie (resp. Jordan) superalgebra. Intuitively, rigidity means that small deformations of the product under the action of the structural group produce an isomorphic algebra. In this paper, we classify all linearly compact simple anti-commutative (resp. commutative) rigid superalgebras. Beyond Lie (resp. Jordan) superalgebras, the complete list includes four series and 22 exceptional superalgebras (resp. 10 exceptional superalgebras). |
| first_indexed | 2024-09-23T13:44:33Z |
| format | Article |
| id | mit-1721.1/115845 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T13:44:33Z |
| publishDate | 2018 |
| publisher | Oxford University Press (OUP) |
| record_format | dspace |
| spelling | mit-1721.1/1158452022-10-01T16:52:21Z Classification of Linearly Compact Simple Rigid Superalgebras Cantarini, N. Kac, Victor Massachusetts Institute of Technology. Department of Mathematics Kac, Victor The notion of an anti-commutative (resp. commutative) rigid superalgebra is a natural generalization of the notion of a Lie (resp. Jordan) superalgebra. Intuitively, rigidity means that small deformations of the product under the action of the structural group produce an isomorphic algebra. In this paper, we classify all linearly compact simple anti-commutative (resp. commutative) rigid superalgebras. Beyond Lie (resp. Jordan) superalgebras, the complete list includes four series and 22 exceptional superalgebras (resp. 10 exceptional superalgebras). 2018-05-24T15:58:35Z 2018-05-24T15:58:35Z 2010-02 2018-05-24T12:45:29Z Article http://purl.org/eprint/type/JournalArticle 1073-7928 1687-0247 http://hdl.handle.net/1721.1/115845 Cantarini, N. and V. G. Kac. “Classification of Linearly Compact Simple Rigid Superalgebras.” International Mathematics Research Notices 17 (February 2010): 3341–3393 © 2010 The Author https://orcid.org/0000-0002-2860-7811 http://dx.doi.org/10.1093/imrn/rnp231 International Mathematics Research Notices Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Oxford University Press (OUP) arXiv |
| spellingShingle | Cantarini, N. Kac, Victor Classification of Linearly Compact Simple Rigid Superalgebras |
| title | Classification of Linearly Compact Simple Rigid Superalgebras |
| title_full | Classification of Linearly Compact Simple Rigid Superalgebras |
| title_fullStr | Classification of Linearly Compact Simple Rigid Superalgebras |
| title_full_unstemmed | Classification of Linearly Compact Simple Rigid Superalgebras |
| title_short | Classification of Linearly Compact Simple Rigid Superalgebras |
| title_sort | classification of linearly compact simple rigid superalgebras |
| url | http://hdl.handle.net/1721.1/115845 https://orcid.org/0000-0002-2860-7811 |
| work_keys_str_mv | AT cantarinin classificationoflinearlycompactsimplerigidsuperalgebras AT kacvictor classificationoflinearlycompactsimplerigidsuperalgebras |