Abstract

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Frobenius-Schur indicators of representations of finite group has been developed 

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and studied for more than a century. The notion has been recently generalized to

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semisimple Hopf algebras or quasi-Hopf algebras, and even to pivotal categories 

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which are not necessarily semisimple. In this talk, we introduce some gauge invariants 

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for each finite dimensional Hopf algebra H. These invariants coincide with the 

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Frobenius-Schur indicators of the regular representation when H is a semisimple 

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complex Hopf algebra. As an application, we demonstrate the inequivalence of the 

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Taft algebras by computing these gauge invariants. 

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Part of this talk is based on joint work with Y. Kashina and S. Montgomery.