Induced modules of semisimple hopf algebras

Hu Jun; Yinhuo Zhang

doi:10.1142/s1005386707000521

Induced modules of semisimple hopf algebras

Hu Jun^*, Yinhuo Zhang

^*Corresponding author for this work

School of Mathematics and Statistics

Victoria University of Wellington

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

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 H_β, 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 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 H_β into a direct sum of simple D(H)-modules.

Original language	English
Pages (from-to)	571-584
Number of pages	14
Journal	Algebra Colloquium
Volume	14
Issue number	4
DOIs	https://doi.org/10.1142/s1005386707000521
Publication status	Published - Dec 2007

Keywords

Character algebra
Drinfel'd double
Hopf algebra

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10.1142/s1005386707000521

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AB - 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 Hβ* 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.

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KW - Hopf algebra

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Induced modules of semisimple hopf algebras

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Keywords

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