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arXiv · 1706.02484

On the algebraic variety of Hom-Lie algebras

Elisabeth Remm·Michel Goze
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Abstract

The set HLie(n) of the n-dimensional Hom-Lie algebras over an algebraically closed field of characteristic zero is provided with a structure of algebraic subvariety of the affine plane of dimension n^2(n-1)/2}. For n=3, these two sets coincide, for n=4 it is an hypersurface in K^{24}. For n>4, we describe the scheme of polynomial equations which define HLie(n). We determine also what are the classes of Hom-Lie algebras which are P-algebras where P is a binary quadratic operads.

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Elisabeth Remm, Michel Goze. 2017-06-08. On the algebraic variety of Hom-Lie algebras. https://arxiv.org/abs/1706.02484

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