Induced Modules of Semisimple Hopf Algebras

• 来源期刊: 代数集刊（英文版）
• 关键词: Hopf algebra character algebra Drinfel'd double
• 年，卷（期）: 2007,（4）
• 页码范围: 571-584
• 页数: 14页
• 语种: 英文

摘要

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, whereβ is a group-like element in H*. Using the commuting pair established in [7], we obtain an analogue of the class equation for H*β 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.