On the von Neumann algebra of class functions on a compact quantum group

Abstract: A famous result of Pytlik states that the radial subalgebra in the group von Neumann algebra of a free group on n>=2 generators is maximal abelian (MASA). One can study an analogue of this subalgebra - the von Neumann algebra generated by characters - in a more general context of discrete quantum groups. By a result of Freslon and Vergnioux, it is known that this algebra is MASA for the discrete quantum group dual to the Kac-type orthogonal quantum group. I will show that the situation is quite different when our compact quantum group is not of Kac type (equivalently, the discrete dual is non-unimodular). The crucial notion for our work is that of quasi-split inclusions. This is a joint work with Mateusz Wasilewski.

functional analysisgroup theoryoperator algebrasquantum algebra

Audience: researchers in the topic

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