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.
Polynomial identities for quivers via incidence algebras / Berele, Allan; Cerulli Irelli, Giovanni; De Loera Chávez, Javier; Pascucci, Elena. - In: BULLETIN OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6093. - (2026).
Polynomial identities for quivers via incidence algebras
Allan Berele;Giovanni Cerulli Irelli
;Elena Pascucci
2026
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.File allegati a questo prodotto
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