Journal of Operator Theory

Volume 52, Issue 1, Summer 2004 pp. 3-20.

Frobenius duality in $C^*$-tensor categories

Authors: Shigeru Yamagami
Author institution: Department of Mathematical Sciences, Ibaraki University, Mito 310-8512, Japan

Summary: Rigidity in $C^*$-tensor categories is investigated from the viewpoint of Frobenius duality. Motivated by our previous studies on Jones index theory in bimodules, the existence and uniqueness are established for Frobenius duality. Similar results are proved for fiber functors, as well, with some applications to compact quantum groups.

Keywords: monoidal category, tensor category, rigidity

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