Polynomial identities for quivers via incidence algebras

TL;DR

The paper demonstrates that the path algebra of a quiver shares polynomial identities with matrix algebras, establishing PI-equivalence for certain quivers and matrix algebras.

Contribution

It establishes a connection between path algebras of quivers and matrix algebras through polynomial identities, providing new insights into their algebraic structure.

Findings

Path algebra of a quiver satisfies the same polynomial identities as matrix algebras.

The algebra of nxn matrices is PI-equivalent to the path algebra of an n-vertex oriented cycle.

Abstract

We show that the path algebra of a quiver satisfies the same polynomial identities of an algebra of matrices, if any. In particular, the algebra of nxn matrices is PI-equivalent to the path algebra of the oriented cycle with n vertices.