Lie nilpotency and Lie solvability of tensor product of multiplicative Lie algebras

Abstract

In this article, we discuss Lie nilpotency and Lie solvability of non-abelian tensor product of multiplicative Lie algebras. In particular, for giving information concerning the Lie nilpotency (or Lie solvability) of either multiplicative Lie algebras $G$ or $H,$ the non-abelian tensor product $\frac{G\otimes H}{I}$ is Lie nilpotent (or Lie solvable), for some ideal $I$ of $G\otimes H$.