Quivers with Polynomial Identities
Abstract
We provide a topological characterization of quivers whose path algebra satisfies a polynomial identity. This class includes the oriented cycle and acyclic quivers and, in the latter case, we describe the associated T-ideal. We introduce a generalization of Arnold’s A-graded algebras, which we call locally A-graded algebras, and prove that they are also PI. We give an example of a quiver algebra satisfying a polynomial identity, even if the path algebra of the quiver does not.
Fields of Study & Subjects
Algebraic structures and combinatorial models
Advanced Combinatorial Mathematics
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- Annals of representation theory
- Volume
- 3
- Issue
- 2
- Pages
- 165–177
- Publication date
- 17 June 2026
- Language
- EN