Frobenius-Schur indicator for categories with duality (Q398538)

Summary: 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 \(C^\ast\)-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 \(\mathrm{SL}_2\).