Polynomial identities, group rings and enveloping algebras

Abstract: I will talk about the development of the theory of polynomial identities initiated by important questions such as Burnside's asking if every finitely generated torsion group is finite. The field was enriched by contributions of many great mathematicians. Most notably Lie rings methods were developed and used by Zelmanov in the 1990s to give a positive solution to the restricted Burnside problem which awarded him the Fields medal. It has been of great interest to expand the theory to other varieties of algebraic structures. In particular, I will review when a group algebra or enveloping algebra satisfy a polynomial identity.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar