On converse of the Schur's theorem for nilpotent Lie superalgebras
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866929500454912000 |
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| author | Shamsaki, A. Niroomand, P. Stitzinger, E. |
| author_facet | Shamsaki, A. Niroomand, P. Stitzinger, E. |
| contents | In this paper, we establish a converse to Schur's theorem for Lie superalgebras \( L \), focusing on cases where the minimal generator number pairs \((p \vert q)\) of \( L/Z(L) \) are considered, and where the superdimension \( \mathrm{sdim} L^{2} \) is finite. We introduce a new invariant \( st(L) \), which plays a key role in the classification of finite-dimensional nilpotent Lie superalgebras. Specifically, we classify the structure of all such Lie superalgebras \( L \) when \( st(L) \in \{(0,0), (1,0), (0,1), (2,0), (0,2), (1,1)\} \). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_10152 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On converse of the Schur's theorem for nilpotent Lie superalgebras Shamsaki, A. Niroomand, P. Stitzinger, E. Commutative Algebra Rings and Algebras 17B30, 17B05, 17B99 In this paper, we establish a converse to Schur's theorem for Lie superalgebras \( L \), focusing on cases where the minimal generator number pairs \((p \vert q)\) of \( L/Z(L) \) are considered, and where the superdimension \( \mathrm{sdim} L^{2} \) is finite. We introduce a new invariant \( st(L) \), which plays a key role in the classification of finite-dimensional nilpotent Lie superalgebras. Specifically, we classify the structure of all such Lie superalgebras \( L \) when \( st(L) \in \{(0,0), (1,0), (0,1), (2,0), (0,2), (1,1)\} \). |
| title | On converse of the Schur's theorem for nilpotent Lie superalgebras |
| topic | Commutative Algebra Rings and Algebras 17B30, 17B05, 17B99 |
| url | https://arxiv.org/abs/2208.10152 |