Year: 2026
Type: article
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.
Source: Annals of representation theory
DOI: 10.5802/art.38
Authors: Giovanni Cerulli Irelli, Javier De Loera Chávez, Elena Pascucci
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4416679458
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