Non-associative Frobenius algebras of type $^1E_6$ with trivial Tits algebras
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866929197060980736 |
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| author | Desmet, Jari |
| author_facet | Desmet, Jari |
| contents | Very recently, Maurice Chayet and Skip Garibaldi have introduced a class of commutative non-associative algebras, for each simple linear algebraic group over an arbitrary field (with some minor restriction on the characteristic).
In a previous paper, we gave an explicit description of these algebras for groups of type $G_2$ and $F_4$ in terms of the octonion algebras and the Albert algebras, respectively. In this paper, we attempt a similar approach for type $E_6$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_06910 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Non-associative Frobenius algebras of type $^1E_6$ with trivial Tits algebras Desmet, Jari Rings and Algebras Group Theory Representation Theory Very recently, Maurice Chayet and Skip Garibaldi have introduced a class of commutative non-associative algebras, for each simple linear algebraic group over an arbitrary field (with some minor restriction on the characteristic). In a previous paper, we gave an explicit description of these algebras for groups of type $G_2$ and $F_4$ in terms of the octonion algebras and the Albert algebras, respectively. In this paper, we attempt a similar approach for type $E_6$. |
| title | Non-associative Frobenius algebras of type $^1E_6$ with trivial Tits algebras |
| topic | Rings and Algebras Group Theory Representation Theory |
| url | https://arxiv.org/abs/2306.06910 |