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arXiv · 2511.03536

Polynomial identities for quivers via incidence algebras

Allan Berele·Giovanni Cerulli Irelli·Javier De Loera Chávez·Elena Pascucci
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Abstract

We show that the path algebra of a quiver satisfies the same polynomial identities of an algebra of matrices, if any. In particular, the algebra of nxn matrices is PI-equivalent to the path algebra of the oriented cycle with n vertices.

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Allan Berele, Giovanni Cerulli Irelli, Javier De Loera Chávez, Elena Pascucci. 2025-11-05. Polynomial identities for quivers via incidence algebras. https://doi.org/10.1112/blms.70369

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