Maximal amenability of the radial subalgebra in free quantum group factors

Abstract

We show that the radial MASA in the orthogonal free quantum group algebra $L\left(F{O}_N\right)$ is maximal amenable if N is large enough, using the Asymptotic Orthogonality Property. This relies on a detailed study of the corresponding bimodule, for which we construct in particular a quantum analogue of Rădulescu's basis. As a byproduct we also obtain the value of the Pukánszky invariant for this MASA.