From the Albert algebra to Kac's ten-dimensional Jordan superalgebra via tensor categories in characteristic 5
2024
Online
report
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
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From the Albert algebra to Kac's ten-dimensional Jordan superalgebra via tensor categories in characteristic 5
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Autor/in / Beteiligte Person: | Elduque, Alberto ; Etingof, Pavel ; Kannan, Arun S. |
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Veröffentlichung: | 2024 |
Medientyp: | report |
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