On the triple tensor product of nilpotent Lie algebras

Abstract

In this paper, we give the explicit structure of ${\otimes }^{3}H$ and ${\wedge }^{3}H$ where $H$ is a generalized Heisenberg Lie algebra of rank at most $2.$ Moreover, for a non-abelian nilpotent Lie algebra $L,$ we obtain an upper bound for the dimension of $ \otimes^{3} L.

Some typo errors are corrected in this version. The final version will be published at journal of Linear and Multilinear Algebras with some revisions on the current version