On the Schur multiplier of nilpotent Lie superalgebra
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909218146091008 |
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| author | Shamsaki, Afsaneh Niroomand, Peyman |
| author_facet | Shamsaki, Afsaneh Niroomand, Peyman |
| contents | Let $L$ be an $(m\vert n)$-dimensional nilpotent Lie superalgebra where $m + n \geq 4$ and $n \geq 1$. This paper classifies such nilpotent Lie superalgebras $L$ with a derived subsuperalgebra of dimension $m+n-2$ such that $γ(L) = m + 2n - 2 - \dim \mathcal{M}(L)$, where $γ(L) \in \{0, 1, 2\}$ and $\mathcal{M}(L)$ denotes the Schur multiplier of $L$. Furthermore, we show that all these superalgebras are capable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_03573 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Schur multiplier of nilpotent Lie superalgebra Shamsaki, Afsaneh Niroomand, Peyman Commutative Algebra 17B30 Let $L$ be an $(m\vert n)$-dimensional nilpotent Lie superalgebra where $m + n \geq 4$ and $n \geq 1$. This paper classifies such nilpotent Lie superalgebras $L$ with a derived subsuperalgebra of dimension $m+n-2$ such that $γ(L) = m + 2n - 2 - \dim \mathcal{M}(L)$, where $γ(L) \in \{0, 1, 2\}$ and $\mathcal{M}(L)$ denotes the Schur multiplier of $L$. Furthermore, we show that all these superalgebras are capable. |
| title | On the Schur multiplier of nilpotent Lie superalgebra |
| topic | Commutative Algebra 17B30 |
| url | https://arxiv.org/abs/2406.03573 |