2012/08/12 by Shimizu, Kenichi
#FOS: Mathematics #Group Theory (math.GR) #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1208.2435
We generalize the Frobenius-Schur theorem to C^*-categories. From this category-theoretical point of view, we introduce the notions of real, complex and quaternionic representations of Hopf C^*-algebras. Based on these definitions, we give another type of the Hopf-algebraic analogue of the Frobenius-Schur theorem, originally due to Linchenko and Montgomery. Also given are similar results for weak Hopf C^*-algebras, table algebras and compact quantum groups.