A note on reduced and von Neumann algebraic free wreath products

  title={A note on reduced and von Neumann algebraic free wreath products},
  author={Jonas Wahl},
  journal={arXiv: Operator Algebras},
  • J. Wahl
  • Published 18 November 2014
  • Mathematics
  • arXiv: Operator Algebras
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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