# Some properties on the tensor square of Lie algebras - Mathematics > Rings and Algebras

Abstract: In the present paper we extend and improve the results of \cite{bl, br} forthe tensor square of Lie algebras. More precisely, for any Lie algebra $L$ with$L-L^2$ of finite dimension, we prove $L\otimes L\cong L\square L\oplus L\wedgeL$ and $Z^{\wedge}L\cap L^2=Z^{\otimes}L$. Moreover, we show that $L\wedgeL$ is isomorphic to derived subalgebra of a cover of $L$, and finally we give afree presentation for it.

Author: Peyman Niroomand

Source: https://arxiv.org/