Nilpotent Lie algebras with two centralizer dimensions over a finite field
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Acceso en línea: | |
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| _version_ | 1866917629089808384 |
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| author | Kundu, Rijubrata Naik, Tushar Kanta Singh, Anupam |
| author_facet | Kundu, Rijubrata Naik, Tushar Kanta Singh, Anupam |
| contents | A result of Barnea and Isaacs states that if $L$ is a finite dimensional nilpotent Lie algebra with exactly two distinct centralizer dimensions, then nilpotency class of $L$ is either $2$ or $3$. In this article, we classify all such finite dimensional $3$-step nilpotent Lie algebras over a finite field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_07676 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Nilpotent Lie algebras with two centralizer dimensions over a finite field Kundu, Rijubrata Naik, Tushar Kanta Singh, Anupam Rings and Algebras Group Theory 17B05, 17B30 A result of Barnea and Isaacs states that if $L$ is a finite dimensional nilpotent Lie algebra with exactly two distinct centralizer dimensions, then nilpotency class of $L$ is either $2$ or $3$. In this article, we classify all such finite dimensional $3$-step nilpotent Lie algebras over a finite field. |
| title | Nilpotent Lie algebras with two centralizer dimensions over a finite field |
| topic | Rings and Algebras Group Theory 17B05, 17B30 |
| url | https://arxiv.org/abs/2208.07676 |