On the homological dimensions of Leavitt path algebras with coefficients in commutative rings

TL;DR

This paper investigates the homological dimensions of Leavitt path algebras over commutative rings, providing bounds and formulas that enhance understanding of their algebraic properties.

Contribution

It offers sharp bounds and a formula for homological dimensions of Leavitt path algebras with coefficients in commutative rings and algebras.

Findings

Established sharp bounds for homological dimensions.

Derived a formula for homological dimensions over commutative unital algebras.

Enhanced understanding of algebraic properties of Leavitt path algebras.

Abstract

In this paper, we give sharp bounds for the homological dimensions of the Leavitt path algebra $L_K(E)$ of a finite graph $E$ with coefficients in a commutative ring $K$, as well as establish a formula for calculating the homological dimensions of $L_K(E)$ when $K$ is a commutative unital algebra over a field.