Some properties on the tensor square of Lie algebras

Details Some properties on the tensor square of Lie algebras Some properties on the tensor square of Lie algebras

2010-06-11

arxiv.org/abs/1006.2240v4

Mathematics

Rings and Algebras

To appear in J. Algebra Appl. with the small revision

Scientific paper

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

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