Endomorphism rings of Leavitt path algebras

TL;DR

This paper explores the properties of endomorphism rings of Leavitt path algebras, identifying conditions for various regularity and invariance properties, and characterizing when these algebras are continuous or automorphism invariant.

Contribution

It provides new criteria for when the endomorphism ring of a Leavitt path algebra has specific regularity and invariance properties, advancing understanding of their algebraic structure.

Findings

Conditions for von Neumann regularity and $ ho$-regularity of endomorphism rings.

Characterization of when Leavitt path algebras are continuous.

Criteria for automorphism invariance of Leavitt path algebras.

Abstract

We investigate conditions under which the endomorphism ring of the Leavitt path algebra $L_{K}(E)$ possesses various ring and module-theoretical properties such as being von Neumann regular, $\pi$-regular, strongly $\pi$-regular or self-injective. We also describe conditions under which $L_{K}(E)$ is continuous as well as automorphism invariant as a right $L_{K}(E)$-module.