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arXiv · 1208.2433

Frobenius-Schur indicator for categories with duality

Kenichi Shimizu
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Abstract

We introduce the Frobenius-Schur indicator for categories with duality to give a category-theoretical understanding of various generalizations of the Frobenius-Schur theorem, including that for semisimple quasi-Hopf algebras, weak Hopf C*-algebras and association schemes. Our framework also clarifies a mechanism how the `twisted' theory arises from the ordinary case. As a demonstration, we give a twisted Frobenius-Schur theorem for semisimple quasi-Hopf algebras. We also give several applications to the quantum SL_2.

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Kenichi Shimizu. 2012-08-12. Frobenius-Schur indicator for categories with duality. https://doi.org/10.3390/axioms1030324

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