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arXiv · 2208.07676

Nilpotent Lie algebras with two centralizer dimensions over a finite field

Rijubrata Kundu·Tushar Kanta Naik·Anupam Singh
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Abstract

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.

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Rijubrata Kundu, Tushar Kanta Naik, Anupam Singh. 2022-08-16. Nilpotent Lie algebras with two centralizer dimensions over a finite field. https://doi.org/10.1016/j.jalgebra.2023.06.013

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