Frobenius-Schur theorem for $C^*$-categories
Representation Theory
2013-03-06 v3 Group Theory
Quantum Algebra
Abstract
We generalize the Frobenius-Schur theorem to -categories. From this category-theoretical point of view, we introduce the notions of real, complex and quaternionic representations of Hopf -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 -algebras, table algebras and compact quantum groups.
Keywords
Cite
@article{arxiv.1208.2435,
title = {Frobenius-Schur theorem for $C^*$-categories},
author = {Kenichi Shimizu},
journal= {arXiv preprint arXiv:1208.2435},
year = {2013}
}
Comments
34 pages. Completely rewritten. The title has been changed since the main result is reformulated in a $C^*$-categorical setting