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.
Quivers with Polynomial Identities / Cerulli Irelli, G., De Loera Chávez, J., Pascucci, E.. - 3:2(2026), pp. 165-177. [10.5802/art.38]
Quivers with Polynomial Identities
Cerulli Irelli, Giovanni
;Pascucci, Elena
2026
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.File allegati a questo prodotto
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