Quivers with Polynomial Identities

2025/08/01 by Irelli, Giovanni Cerulli, Chávez, Javier De Loera, Pascucci, Elena · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2508.00662

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.

Citations

• Graded polynomial identities of the infinite-dimensional upper triangular matrices over an arbitrary field
• Leavitt path algebras with finitely presented irreducible\n representations
• Leavitt path algebras satisfying a polynomial identity
• Finitely presented simple modules over Leavitt path algebras
• Leavitt Path Algebras of Finite Gelfand-Kirillov Dimension

Cited by

• Polynomial identities for quivers via incidence algebras

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