On the Dimensions of Path Algebras

TL;DR

This paper investigates the representation and derived dimensions of path algebras associated with finite, acyclic quivers over artin algebras, providing insights into their algebraic complexity.

Contribution

It offers new results on the dimensions of path algebras related to acyclic quivers, expanding understanding in algebra representation theory.

Findings

Determined bounds for the representation dimension of path algebras.

Established relationships between derived dimension and quiver properties.

Provided classifications for specific classes of path algebras.

Abstract

In this paper we study the representation dimension as well as the derived dimension of the path algebra of an artin algebra over a finite and acyclic quiver.