Ring Theory Seminar

Ehsaan Hossain, Department of Pure Mathematics, University of Waterloo

“Group rings: definition and examples”

This semester we’ll be learning group rings and Hopf algebras. It is a longstanding conjec- ture of Kaplansky that if G is a torsion-free group then K[G] is a domain. There are partial results for various classes of groups, treating idempotents as a precursor to zero divisors. One of our first goals will be finiteness in K[G]: if ab = 1, then ba = 1. It will be a long road, but we’ll make if we just believe in ourselves and eat balanced breakfasts daily. We’ll start with the simple definition and some examples. The textbook for group rings will be Passman’s Algebraic Structure of Group Rings, and for Hopf algebras you’d better ask Hongdi.

MC 5403