Nilpotent Lie Algebras of breadth type $(0,3)$
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866917629070934016 |
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| author | Kundu, Rijubrata Naik, Tushar Kanta Singh, Anupam |
| author_facet | Kundu, Rijubrata Naik, Tushar Kanta Singh, Anupam |
| contents | For a natural number $m$, a Lie algebra $L$ over a field $k$ is said to be of breadth type $(0, m)$ if the co-dimension of the centralizer of every non-central element is of dimension $m$. In this article, we classify finite dimensional nilpotent Lie algebras of breadth type $(0, 3)$ over $\mathbb F_q$ of odd characteristics up to isomorphism. We also give a partial classification of the same over finite fields of even characteristic, $\mathbb C$ and $\mathbb R$. We also discuss $2$-step nilpotent Camina Lie algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_04968 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Nilpotent Lie Algebras of breadth type $(0,3)$ Kundu, Rijubrata Naik, Tushar Kanta Singh, Anupam Rings and Algebras 17B05, 17B30 For a natural number $m$, a Lie algebra $L$ over a field $k$ is said to be of breadth type $(0, m)$ if the co-dimension of the centralizer of every non-central element is of dimension $m$. In this article, we classify finite dimensional nilpotent Lie algebras of breadth type $(0, 3)$ over $\mathbb F_q$ of odd characteristics up to isomorphism. We also give a partial classification of the same over finite fields of even characteristic, $\mathbb C$ and $\mathbb R$. We also discuss $2$-step nilpotent Camina Lie algebras. |
| title | Nilpotent Lie Algebras of breadth type $(0,3)$ |
| topic | Rings and Algebras 17B05, 17B30 |
| url | https://arxiv.org/abs/2111.04968 |