# A note on reduced and von Neumann algebraic free wreath products

@article{Wahl2014ANO, title={A note on reduced and von Neumann algebraic free wreath products}, author={Jonas Wahl}, journal={arXiv: Operator Algebras}, year={2014} }

In this paper, we study operator algebraic properties of the reduced and von Neumann algebraic versions of the free wreath products $\mathbb G \wr_* S_N^+$, where $\mathbb G$ is a compact matrix quantum group. Based on recent result on their corepresentation theory by Lemeux and Tarrago, we prove that $\mathbb G \wr_* S_N^+$ is of Kac type whenever $\mathbb G$ is, and that the reduced version of $\mathbb G \wr_* S_N^+$ is simple with unique trace state whenever $N \geq 8$. Moreover, we prove…

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