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arXiv · 1208.2435

Frobenius-Schur theorem for $C^*$-categories

Kenichi Shimizu
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Abstract

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.

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Kenichi Shimizu. 2012-08-12. Frobenius-Schur theorem for $C^*$-categories. https://arxiv.org/abs/1208.2435

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