Pure Math Colloquium

David Riley, Western University

"Hopf algebra actions, gradings, and identical relations"

I will begin by discussing how and when the action of a Hopf algebra H on an algebra A can be viewed as a grading of A. For example, if G is a finite group and H is the dual of the group algebra K[G], then A is an H-algebra precisely when A is group-graded by G. I will then discuss the identical relations of an algebra with a Hopf algebra action. In particular, I will address the following question: when does the existence of an H-identity on A imply the existence of an ordinary polynomial identity on A?

M3 3103