Frobenius–Schur Indicator for Categories with Duality
Graduate School of Mathematics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan
Axioms 2012, 1(3), 324-364; https://doi.org/10.3390/axioms1030324
Submission received: 2 July 2012
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Revised: 23 August 2012
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Accepted: 29 September 2012
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Published: 23 October 2012
(This article belongs to the Special Issue Hopf Algebras, Quantum Groups and Yang-Baxter Equations)
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 of how the “twisted” theory arises from the ordinary case. As a demonstration, we establish twisted versions of the Frobenius–Schur theorem for various algebraic objects. We also give several applications to the quantum SL2.
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MDPI and ACS Style
Shimizu, K. Frobenius–Schur Indicator for Categories with Duality. Axioms 2012, 1, 324-364. https://doi.org/10.3390/axioms1030324
AMA Style
Shimizu K. Frobenius–Schur Indicator for Categories with Duality. Axioms. 2012; 1(3):324-364. https://doi.org/10.3390/axioms1030324
Chicago/Turabian StyleShimizu, Kenichi. 2012. "Frobenius–Schur Indicator for Categories with Duality" Axioms 1, no. 3: 324-364. https://doi.org/10.3390/axioms1030324
