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arXiv · 2201.03034

Kurosh theorem for certain Koszul Lie algebras

Simone Blumer
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Abstract

The Kurosh theorem for groups provides the structure of any subgroup of a free product of groups and its proof relies on Bass-Serre theory of groups acting on trees. In the case of Lie algebras, such a general theory does not exists and the Kurosh theorem is false in general, as it was first noticed by Shirshov. However, we prove that, for a class of positively graded Lie algebras satisfying certain local properties in cohomology, such a structure theorem holds true for subalgebras generated in degree 1. Such class consists of Lie algebras, which have all the subalgebras generated in degree $1$ that are Koszul.

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Simone Blumer. 2022-01-09. Kurosh theorem for certain Koszul Lie algebras. https://arxiv.org/abs/2201.03034

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