Open AccessThis article is
- freely available
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
Article StatisticsClick here to load and display the download statistics.
Notes: Multiple requests from the same IP address are counted as one view.
Cite This Article
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.