A Talented Monoid View on Lie Bracket Algebras over Leavitt Path Algebras

TL;DR

This paper explores the properties of Lie bracket algebras derived from Leavitt path algebras, linking algebraic simplicity with graph-theoretic structures using the talented monoid and Gelfand-Kirillov dimension.

Contribution

It introduces a novel approach connecting the simplicity of Leavitt path algebras with their Lie bracket counterparts through talented monoids and classification tools.

Findings

Connected graded simplicity with Lie algebra properties

Classified nilpotency and solvability using Gelfand-Kirillov dimension

Provided new insights into algebraic structures from graph-based algebras

Abstract

In this article, we study properties as simplicity, solvability and nilpotency for Lie bracket algebras arising from Leavitt path algebras, based on the talented monoid of the underlying graph. We show that graded simplicity and simplicity of the Leavitt path algebra can be connected via the Lie bracket algebra. Moreover, we use the Gelfand-Kirillov dimension for the Leavitt path algebra for a classification of nilpotency and solvability.