Induced Modules of Semisimple Hopf Algebras

Abstract

Let K be a field. Let H be a finite-dimensional K-Hopf algebra and D(H) be the Drinfel'd double of H. In this paper, we study Radford's induced module Hβ, where β is a group-like element in H∗. Using the commuting pair established in [7], we obtain an analogue of the class equation for [Formula: see text] when H is semisimple and cosemisimple. In case H is a finite group algebra or a factorizable semisimple cosemisimple Hopf algebra, we give an explicit decomposition of each Hβ into a direct sum of simple D(H)-modules.