Invariant states on the wreath product
Abstract
Description
Let $\mathfrak{S}_\infty$ be the infinity permutation group and $Γ$ be a separable topological group.
The wreath product $Γ\wr \mathfrak{S}_\infty$ is the semidirect product $Γ^\infty_e \rtimes \mathfrak{S}_\infty$ for the usual permutation action of $\mathfrak{S}_\infty$ on $Γ^\infty_e=\{[γ_i]_{i=1}^\infty : γ_i\in Γ,\textit{only finitely many}γ_i\neq e\}$. In this paper we obtain the full description of indecomposable states $φ$ on the group $Γ\wr\mathfrak{S}_\infty,$ satisfying the condition: φ(sgs^{-1})=
φ(g)\text{for each}g\in Γ\wr \mathfrak{S}_\infty,s\in\mathfrak{S}_\infty.
37 pages
37 pages