On Jordan algebras that are factors of Matsuo algebras
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866911882777985024 |
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| author | Gorshkov, Ilya Mamontov, Andrey Staroletov, Alexey |
| author_facet | Gorshkov, Ilya Mamontov, Andrey Staroletov, Alexey |
| contents | We describe all finite connected 3-transposition groups whose Matsuo algebras have nontrivial factors that are Jordan algebras. As a corollary, we show that if F is a field of characteristic 0, then there exist infinitely many primitive axial algebras of Jordan type 1/2 over F that are not factors of Matsuo algebras. As an illustrative example, we prove this for an exceptional Jordan algebra over F. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_10958 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Jordan algebras that are factors of Matsuo algebras Gorshkov, Ilya Mamontov, Andrey Staroletov, Alexey Rings and Algebras Group Theory 17A99, 20F29 We describe all finite connected 3-transposition groups whose Matsuo algebras have nontrivial factors that are Jordan algebras. As a corollary, we show that if F is a field of characteristic 0, then there exist infinitely many primitive axial algebras of Jordan type 1/2 over F that are not factors of Matsuo algebras. As an illustrative example, we prove this for an exceptional Jordan algebra over F. |
| title | On Jordan algebras that are factors of Matsuo algebras |
| topic | Rings and Algebras Group Theory 17A99, 20F29 |
| url | https://arxiv.org/abs/2305.10958 |