Séminaires : Séminaire d'Algèbre

Seventy-five years have passed since Amitsur and Levitzki proved that the algebra of n x n matrices satisfies the standard polynomial identity of degree 2n. Since then, mathematicians have investigated algebras whose elements satisfy a polynomial identity, meaning that every substitution of elements of the algebra into a given noncommutative polynomial yields zero. Such algebras are known as PI algebras.

The theory of PI algebras has developed enormously over the years, leading to deep and far-reaching results. In this talk, we address the following natural questions: which quivers have a path algebra that is PI? What can be said about the corresponding T-ideal of polynomial identities? And how does the situation change when relations are imposed on the path algebra?

This is joint work with Elena Pascucci and Javier De Loera Chávez.

This talk will take in hybrid mode at the Institut Henri Poincaré.