Hongdi Huang, Department of Pure Mathematics, University of Waterloo
“Maschke’s Theorem in Hopf algebra.”
First recall the classical Maschke’s Theorem for group algebras: If G is a finite group then kG is semisimple if and only if |G| ̸= 0 ∈ k. Our goal this week is to translate this result into the language of integrals for any finite dimensional Hopf algebra. Namely, we shall see that if H is any finite dimensional Hopf algebra then H is semisimple if and only if H has no left integral or no right intergral. We will introduce the the concepts of Hopf modules and intergrals.
MC 5403