Graphs of C*-algebras and free wreath products of quantum groups

Arthur TROUPEL (Université Paris Cité)

Thursday 23rd November, 2023 16:00-17:00 Maths 311B

Abstract

The free wreath product of a compact quantum group by the quantum permutation group S_N^+ has been introduced by Bichon in order to give a quantum counterpart of the classical wreath product. The representation theory of such quantum groups is well-known, as well as some approximation properties, but some results about their operator algebras were still open, for example stability of Haagerup property, of K-amenability or factoriality of the von Neumann algebra. I will present a joint work with Pierre Fima in which we identify these algebras with the fundamental C*-algebras of certain graphs of C*-algebras, and we deduce such properties from these constructions.

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