Ergodic coactions with large multiplicity and monoidal equivalence of quantum groups

Abstract

We construct new examples of ergodic coactions of compact quantum groups, in which the multiplicity of an irreducible corepresentation can be strictly larger than the dimension of the latter. These examples are obtained using a bijective correspondence between certain ergodic coactions on C*-algebras and unitary fiber functors on the representation category of a compact quantum group. We classify these unitary fiber functors on the universal orthogonal and unitary quantum groups. The associated C*-algebras and von Neumann algebras can be defined by generators and relations, but are not yet well understood.

After completion of a first version of this paper, signed by the last two authors, the first author joined the project and his preprint [6] was taken into account, yielding the current paper as a final result

References in corpus (2)

• Ergodic Actions of Universal Quantum Groups on Operator Algebras
• A Remark on Quantum Group Actions and Nuclearity

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