Polynomial identities for quivers via incidence algebras
Representation Theory
2026-05-15 v2 Combinatorics
Rings and Algebras
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.
Cite
@article{arxiv.2511.03536,
title = {Polynomial identities for quivers via incidence algebras},
author = {Allan Berele and Giovanni Cerulli Irelli and Javier De Loera Chávez and Elena Pascucci},
journal= {arXiv preprint arXiv:2511.03536},
year = {2026}
}
Comments
4 pages