On the triple tensor product of nilpotent Lie algebras

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.