Vol. 6, No. 2, 2012

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Fusion rules for abelian extensions of Hopf algebras

Christopher Goff

Vol. 6 (2012), No. 2, 327–339
Abstract

We investigate the representation theory and fusion rules of a class of cocentral abelian (quasi-)Hopf extensions of Hopf algebras which includes twisted (generalized) quantum doubles of finite groups, and a certain quasi-Hopf algebra of Schauenburg associated to group-theoretical fusion categories. We then present a nontrivial example with noncommutative fusion rules.

Keywords
fusion rules, Hopf algebras, quasi-Hopf, abelian extensions, group-theoretical fusion categories
Mathematical Subject Classification 2000
Primary: 16S40, 18D10
Secondary: 16W30
Milestones
Received: 19 August 2010
Revised: 28 February 2011
Accepted: 10 April 2011
Published: 24 June 2012
Authors
Christopher Goff
Mathematics Department
University of the Pacific
3601 Pacific Avenue
Stockton, CA 95211
United States