On the triple tensor product of nilpotent Lie algebras

TL;DR

This paper explicitly describes the structure of triple tensor and wedge products of certain nilpotent Lie algebras, providing bounds on their dimensions, advancing understanding of their algebraic properties.

Contribution

It offers explicit structures for triple tensor and wedge products of generalized Heisenberg Lie algebras and bounds their dimensions for non-abelian nilpotent Lie algebras.

Findings

Explicit structure of $ \otimes^{3} H $ and $ \wedge^{3} H $ for generalized Heisenberg Lie algebras

Upper bounds for the dimension of $ \otimes^{3} L $ in non-abelian nilpotent Lie algebras

Enhanced understanding of tensor products in nilpotent Lie algebra theory

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.