On extensions of Lie algebras

TL;DR

This paper introduces a new construction of Lie algebras that parallels the wreath product of groups, demonstrating that any extension of Lie algebras can be embedded into this construction.

Contribution

It presents a novel Lie algebra construction analogous to the wreath product, extending the embedding property known for groups to Lie algebras.

Findings

The construction has properties similar to the wreath product of groups.

Any extension of Lie algebras can be embedded into this new construction.

The method generalizes the embedding of group extensions to Lie algebra extensions.

Abstract

In the note some construction of Lie algebras is introduced. It is proved that the construction has the same property as a well known wreath product of groups [1]: Any extension of groups can be embedded into their wreath product [2].