تقرير
Matsuo algebras in characteristic 2
| العنوان: | Matsuo algebras in characteristic 2 |
|---|---|
| المؤلفون: | De Medts, Tom, Stout, Mathias |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Group Theory, Mathematics - Rings and Algebras, 20B25, 20F29, 17A99, 51E30 |
| الوصف: | 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 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2308.11360 |
| رقم الأكسشن: | edsarx.2308.11360 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |