Ring Theory Seminar
Speaker: Elena Pascucci (Sapienza Università di Roma)
Title: A Glimpse into Quivers and Identities
Date: 15/10/2025
Time: 10:00
Web: http://mat.uab.cat/web/ligat/
Abstract: A polynomial identity for an algebra $A$ is a polynomial in non-commutative variables that vanishes under all evaluations in $A$. Algebras satisfying at least one such non-trivial identity are known as PI-algebras.
In this talk, we focus on a particular class of algebras arising from quiver theory: path algebras. Our main goal is to provide a topological characterization of quivers whose path algebras satisfy a polynomial identity. In certain cases, we will describe the explicit identities that arise, and we will also discuss extensions of these results to quivers with relations.
This is based on a joint work with Giovanni Cerulli Irelli and Javier De Loera Chávez.