no. 2
Quivers with Polynomial Identities
Cerulli Irelli, Giovanni1; De Loera Chávez, Javier2; Pascucci, Elena2, 3
1Dipartimento SBAI, Sapienza Università di Roma, Via Scarpa 10, 00161, Roma, Italy
2Dipartimento SBAI, Sapienza Università di Roma, Via Scarpa 16, 00161, Roma, Italy
3CMUP, Departamento de Matemática, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal
Annals of Representation Theory, Volume 3 (2026) no. 2, pp. 165-177

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.

Received:
Accepted:
Published online:
DOI: 10.5802/art.38
Classification: 16R10, 16G20
Keywords: Polynomial Identities, Quivers, Path Algebras

Cerulli Irelli, Giovanni  1 ; De Loera Chávez, Javier  2 ; Pascucci, Elena  2 , 3

1 Dipartimento SBAI, Sapienza Università di Roma, Via Scarpa 10, 00161, Roma, Italy
2 Dipartimento SBAI, Sapienza Università di Roma, Via Scarpa 16, 00161, Roma, Italy
3 CMUP, Departamento de Matemática, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
Cerulli Irelli, Giovanni; De Loera Chávez, Javier; Pascucci, Elena. Quivers with Polynomial Identities. Annals of Representation Theory, Volume 3 (2026) no. 2, pp. 165-177. doi: 10.5802/art.38
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