Matsuo algebras in characteristic 2
| Autor: | De Medts, Tom, Stout, Mathias |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | We extend the theory of Matsuo algebras, which are certain non-associative algebras related to 3-transposition groups, to characteristic 2. Instead of idempotent elements associated to points in the corresponding Fischer space, our algebras are now generated by nilpotent elements associated to lines. For many 3-transposition groups, this still gives rise to a $\mathbb{Z}/2\mathbb{Z}$-graded fusion law, and we provide a complete classification of when this occurs. In one particular small case, arising from the 3-transposition group $\operatorname{Sym}(4)$, the fusion law is even stronger, and the resulting Miyamoto group is an algebraic group $\mathbb{G}_a^2 \rtimes \mathbb{G}_m$. Comment: 19 pages |
| Databáze: | arXiv |
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