On the Frobenius–Schur indicators for quasi-Hopf algebras

Abstract

Mason and Ng have given a generalization to semisimple quasi-Hopf algebras of Linchenko and Montgomery's generalization to semisimple Hopf algebras of the classical Frobenius–Schur theorem for group representations. We give a simplified proof, in particular a somewhat conceptual derivation of the appropriate form of the Frobenius–Schur indicator that indicates if and in which of two possible fashions a given simple module is self-dual.