Double extensions for quadratic Hom-Lie algebras with equivariant twist maps
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914940786311168 |
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| author | García-Delgado, R. Salgado, G. Sánchez-Valenzuela, O. A. |
| author_facet | García-Delgado, R. Salgado, G. Sánchez-Valenzuela, O. A. |
| contents | Quadratic Hom-Lie algebras with equivariant twist maps are studied. They are completely characterized in terms of a maximal proper ideal that contains the kernel of the twist map and a complementary subspace to it that is either 1-dimensional, or has the structure of a simple Lie algebra. It is shown how the analogue of the double extension construction works well for quadratic Hom-Lie algebras with equivariant twist maps and prove that any indecomposable and quadratic Hom-Lie algebra with equivariant and nilpotent twist map can be identified with such a double extension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_06888 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Double extensions for quadratic Hom-Lie algebras with equivariant twist maps García-Delgado, R. Salgado, G. Sánchez-Valenzuela, O. A. Rings and Algebras 17B61, 17B30 (Primary) 17A30, 17B60, 17D30 (Secondary) Quadratic Hom-Lie algebras with equivariant twist maps are studied. They are completely characterized in terms of a maximal proper ideal that contains the kernel of the twist map and a complementary subspace to it that is either 1-dimensional, or has the structure of a simple Lie algebra. It is shown how the analogue of the double extension construction works well for quadratic Hom-Lie algebras with equivariant twist maps and prove that any indecomposable and quadratic Hom-Lie algebra with equivariant and nilpotent twist map can be identified with such a double extension. |
| title | Double extensions for quadratic Hom-Lie algebras with equivariant twist maps |
| topic | Rings and Algebras 17B61, 17B30 (Primary) 17A30, 17B60, 17D30 (Secondary) |
| url | https://arxiv.org/abs/2304.06888 |