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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.13710 |
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| _version_ | 1866911764397948928 |
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| author | Albuquerque, Helena Barreiro, Elisabete Calderón, Antonio J. Sánchez, José M. |
| author_facet | Albuquerque, Helena Barreiro, Elisabete Calderón, Antonio J. Sánchez, José M. |
| contents | We introduce the class of split regular Hom-Lie superalgebras as the natural extension of the one of split Hom-Lie algebras and Lie superalgebras, and study its structure by showing that an arbitrary split regular Hom-Lie superalgebra ${\frak L}$ is of the form ${\frak L} = U + \sum_j I_j$ with $U$ a linear subspace of a maximal abelian graded subalgebra $H$ and any $I_j$ a well described (split) ideal of ${\frak L}$ satisfying $[I_j,I_k] = 0$ if $j \neq k$. Under certain conditions, the simplicity of ${\frak L}$ is characterized and it is shown that ${\frak L}$ is the direct sum of the family of its simple ideals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13710 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On split regular Hom-Lie superalgebras Albuquerque, Helena Barreiro, Elisabete Calderón, Antonio J. Sánchez, José M. Rings and Algebras We introduce the class of split regular Hom-Lie superalgebras as the natural extension of the one of split Hom-Lie algebras and Lie superalgebras, and study its structure by showing that an arbitrary split regular Hom-Lie superalgebra ${\frak L}$ is of the form ${\frak L} = U + \sum_j I_j$ with $U$ a linear subspace of a maximal abelian graded subalgebra $H$ and any $I_j$ a well described (split) ideal of ${\frak L}$ satisfying $[I_j,I_k] = 0$ if $j \neq k$. Under certain conditions, the simplicity of ${\frak L}$ is characterized and it is shown that ${\frak L}$ is the direct sum of the family of its simple ideals. |
| title | On split regular Hom-Lie superalgebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2401.13710 |