From octonions to composition superalgebras via tensor categories
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866918094171013120 |
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| author | Daza-Garcia, Alberto Elduque, Alberto Sayin, Umut |
| author_facet | Daza-Garcia, Alberto Elduque, Alberto Sayin, Umut |
| contents | The nontrivial unital composition superalgebras, of dimension 3 and 6, which exist only in characteristic 3, are obtained from the split Cayley algebra and its order 3 automorphisms, by means of the process of semisimplification of the symmetric tensor category of representations of the cyclic group of order 3. Connections with the extended Freudenthal Magic Square in characteristic 3, that contains some exceptional Lie superalgebras specific of this characteristic are discussed too. In the process, precise recipes to go from (nonassociative) algebras in this tensor category to the corresponding superalgebras are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_06559 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | From octonions to composition superalgebras via tensor categories Daza-Garcia, Alberto Elduque, Alberto Sayin, Umut Quantum Algebra Rings and Algebras 17A75 The nontrivial unital composition superalgebras, of dimension 3 and 6, which exist only in characteristic 3, are obtained from the split Cayley algebra and its order 3 automorphisms, by means of the process of semisimplification of the symmetric tensor category of representations of the cyclic group of order 3. Connections with the extended Freudenthal Magic Square in characteristic 3, that contains some exceptional Lie superalgebras specific of this characteristic are discussed too. In the process, precise recipes to go from (nonassociative) algebras in this tensor category to the corresponding superalgebras are given. |
| title | From octonions to composition superalgebras via tensor categories |
| topic | Quantum Algebra Rings and Algebras 17A75 |
| url | https://arxiv.org/abs/2205.06559 |