From the Albert algebra to Kac's ten-dimensional Jordan superalgebra via tensor categories in characteristic 5
| Autor: | Elduque, Alberto, Etingof, Pavel, Kannan, Arun S. |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jalgebra.2024.12.006 |
| Popis: | Kac's ten-dimensional simple Jordan superalgebra over a field of characteristic 5 is obtained from a process of semisimplification, via tensor categories, from the exceptional simple Jordan algebra (or Albert algebra), together with a suitable order 5 automorphism. This explains McCrimmon's 'bizarre result' asserting that, in characteristic 5, Kac's superalgebra is a sort of 'degree 3 Jordan superalgebra'. As an outcome, the exceptional simple Lie superalgebra el(5;5), specific of characteristic 5, is obtained from the simple Lie algebra of type $E_8$ and an order 5 automorphism. In the process, precise recipes to obtain superalgebras from algebras in the category of representations of the cyclic group $C_p$, over a field of characteristic $p>2$, are given. Comment: 22 pages |
| Databáze: | arXiv |
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