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Frobenius–Schur Indicator for Categories with Duality
Graduate School of Mathematics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan
Received: 2 July 2012; in revised form: 23 August 2012 / Accepted: 29 September 2012 / Published: 23 October 2012
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.
Keywords: Frobenius–Schur indicator; category with duality; Hopf algebra; quantum groups
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MDPI and ACS Style
Shimizu, K. Frobenius–Schur Indicator for Categories with Duality. Axioms 2012, 1, 324-364.
Shimizu K. Frobenius–Schur Indicator for Categories with Duality. Axioms. 2012; 1(3):324-364.
Shimizu, Kenichi. 2012. "Frobenius–Schur Indicator for Categories with Duality." Axioms 1, no. 3: 324-364.