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arXiv · 2109.12444

Solvable Lie algebras derived from Lie hyperalgebras

Hesam Safa·Morteza Norouzi
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Abstract

Recently in \cite{s-n}, we have investigated Lie algebras and abelian Lie algebras derived from Lie hyperalgebras using the fundamental relations $\mathcal{L}$ and $\mathcal{A}$, respectively. In the present paper, continuing this method we obtain solvable Lie algebras from Lie hyperalgebras by $\mathcal{S}_n$-relations. We show that $\bigcap_{n\geq 1}\mathcal{S}^*_n$ is the smallest equivalence relation on a Lie hyperalgebra such that the quotient structure is a solvable Lie algebra. We also provide some necessary and sufficient conditions for transitivity of the relation $\mathcal{S}_n$ using the notion of $\mathcal{S}_n$-part.

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Hesam Safa, Morteza Norouzi. 2021-09-25. Solvable Lie algebras derived from Lie hyperalgebras. https://arxiv.org/abs/2109.12444

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