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arXiv · 2508.00662

Quivers with Polynomial Identities

Giovanni Cerulli Irelli·Javier De Loera Chávez·Elena Pascucci
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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.

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Giovanni Cerulli Irelli, Javier De Loera Chávez, Elena Pascucci. 2025-08-01. Quivers with Polynomial Identities. https://arxiv.org/abs/2508.00662

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