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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2303.17993 |
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| _version_ | 1866916845719650304 |
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| author | Beites, Patricia D. Córdova-Martínez, Alejandra S. Cunha, Isabel Elduque, Alberto |
| author_facet | Beites, Patricia D. Córdova-Martínez, Alejandra S. Cunha, Isabel Elduque, Alberto |
| contents | S-structures on Lie algebras, introduced by Vinberg, represent a broad generalization of the notion of gradings by abelian groups. Gradings by, not necessarily reduced, root systems provide many examples of natural S-structures. Here we deal with a situation not covered by these gradings: the short (SL2xSL2)-structures, where the reductive group is the simplest semisimple but not simple reductive group. The algebraic objects that coordinatize these structures are the J-ternary algebras of Allison, endowed with a nontrivial idempotent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_17993 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Short (SL2xSL2)-structures on Lie algebras Beites, Patricia D. Córdova-Martínez, Alejandra S. Cunha, Isabel Elduque, Alberto Rings and Algebras 17B70 S-structures on Lie algebras, introduced by Vinberg, represent a broad generalization of the notion of gradings by abelian groups. Gradings by, not necessarily reduced, root systems provide many examples of natural S-structures. Here we deal with a situation not covered by these gradings: the short (SL2xSL2)-structures, where the reductive group is the simplest semisimple but not simple reductive group. The algebraic objects that coordinatize these structures are the J-ternary algebras of Allison, endowed with a nontrivial idempotent. |
| title | Short (SL2xSL2)-structures on Lie algebras |
| topic | Rings and Algebras 17B70 |
| url | https://arxiv.org/abs/2303.17993 |