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Weak Morita equivalence of compact quantum groups

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OAS - Operator algebras: subfactors and their applications

Motivated by the 2-categorical interpretation of constructs in subfactor theory, Müger introduced the notion of weak Morita equivalence for tensor categories. This relation roughly says that the tensor categories have the same quantum double, or the same “representation theory”. We give a characterization of this equivalence relation for representation categories of compact quantum groups in terms of certain commuting actions. This extends a similar characterization of monoidal equivalence due to Schauenburg and Bichon-De Rijdt-Vaes. Based on joint work with Sergey Neshveyev.



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