Free wreath products by finite group duals
Let $\mathbb G$ be a compact quantum group and let $Λ$ be a finite group. We study $\mathbb W(\mathbb G,Λ):=\mathbb G\wr_{*,β_Λ}\widehatΛ$, a natural family parallel to Bichon's free wreath products $\mathbb G\wr_*S_N^+$. We obtain an explicit formula for the Haar state of $\mathbb W(\mathbb G,Λ)$. Under natural Kac-type factoriality assumptions, we also derive central decompositions of the associated von Neumann and reduced C*-algebras, with full ${\rm II}_1$-factor and simple unique-trace summands.
math.OA↗