Universal equivalence of partially commutative metabelian Lie algebras

TL;DR

This paper establishes criteria for when partially commutative Lie algebras with tree-structured defining graphs are universally equivalent and provides explicit bases for these metabelian Lie algebras.

Contribution

It introduces a criterion for universal equivalence and constructs bases for partially commutative metabelian Lie algebras with tree graphs.

Findings

Criteria for universal equivalence of these Lie algebras

Explicit bases for partially commutative metabelian Lie algebras

Characterization of algebraic properties based on graph structure

Abstract

In this paper, we find a criterium for universal equivalence of partially commutative Lie algebras whose defining graphs are trees. Besides, we obtain bases for partially commutative metabelian Lie algebras.