Quivers with Polynomial Identities
Representation Theory
2025-09-03 v2 Combinatorics
Rings and Algebras
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.
Cite
@article{arxiv.2508.00662,
title = {Quivers with Polynomial Identities},
author = {Giovanni Cerulli Irelli and Javier De Loera Chávez and Elena Pascucci},
journal= {arXiv preprint arXiv:2508.00662},
year = {2025}
}
Comments
13 pages. V2 contains references [9] and [15] concerning Leavitt path algebras, Lemma 6.7 with an example of an infinite quiver and open question 6.9