Frobenius-Schur indicator for categories with duality
arXiv:1208.2433 · doi:10.3390/axioms1030324
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.
38 pages; final version published in the Special Issue on "Hopf Algebras, Quantum Groups and Yang-Baxter Equations" of Axioms