J-ternary algebras, structurable algebras, and Lie superalgebras
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911507523043328 |
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| author | Cunha, Isabel Elduque, Alberto |
| author_facet | Cunha, Isabel Elduque, Alberto |
| contents | A Lie superalgebra is attached to any finite-dimensional J-ternary algebra over an algebraically closed field of characteristic 3, using a process of semisimplification via tensor categories. Some of the exceptional simple Lie algebras, specific of this characteristic, are obtained in this way from J-ternary algebras coming from structurable algebras and, in particular, a new magic square of Lie superalgebras is constructed, with entries depending on a pair of composition algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_18486 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | J-ternary algebras, structurable algebras, and Lie superalgebras Cunha, Isabel Elduque, Alberto Rings and Algebras Primary 17B60, Secondary 17B25, 17B50, 17A30 A Lie superalgebra is attached to any finite-dimensional J-ternary algebra over an algebraically closed field of characteristic 3, using a process of semisimplification via tensor categories. Some of the exceptional simple Lie algebras, specific of this characteristic, are obtained in this way from J-ternary algebras coming from structurable algebras and, in particular, a new magic square of Lie superalgebras is constructed, with entries depending on a pair of composition algebras. |
| title | J-ternary algebras, structurable algebras, and Lie superalgebras |
| topic | Rings and Algebras Primary 17B60, Secondary 17B25, 17B50, 17A30 |
| url | https://arxiv.org/abs/2506.18486 |