Projective representations for compact quantum groups

Ruben Martos

*(University of Copenhagen)*

16:00-17:00, April 12, 2022 Zoom Meeting ID: 693 7501 5439 (Passcode: 640641)

__Abstract:__

In this talk I will present a joint work with K. De Commer and R. Nest. The theory of projective representations for quantum groups was formalised with the notion of "Galois co-object" by K. De Commer ten years ago. An interesting class of such objects are the so-called ¡°cleft" ones and an open question since his work is whether any Galois co-object associated to a compact quantum group is cleft. We answer this question in the affirmative. In particular, this allows us to characterise the torsion of projective type of a compact quantum group in terms of its projective representations in an analogous manner to the case of classical compact groups. A remarkable application of this characterization is the definition of the Baum-Connes assembly map for discrete quantum groups whose torsion is of projective type.

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