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{\Large Department of Mathematics, BGU}

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{\Huge BGU Probability and Ergodic Theory  (PET) seminar}\\[0.2\baselineskip]

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\textbf{On} \emph{Thursday, October 21, 2021}
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\textbf{At} \emph{11:10 -- 12:00}
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\textbf{In} \emph{Building 34, room 14}

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{\large\scshape Tattwamasi Amrutam 
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  (Ben-Gurion University)
}
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will talk about
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{\Large\bfseries Intermediate subalgebras of commutative crossed products of discrete group actions.\par}
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\textsc{Abstract:}
In this talk, we shall focus our attention on intermediate subalgebras of $C(X)\rtimes_r\Gamma$ (and $L^{\infty}(X,\nu)\ltimes\Gamma$).  We begin by describing the construction of the commutative crossed product $C(X)\rtimes_r\Gamma$ and how the group contributes to its structure. We shall talk about various (generalized) averaging properties in this context. As a first application, we will show that every intermediate $C^*$-subalgebra $\mathcal{A}$ of the form $C(Y)\rtimes_r\Gamma\subseteq\mathcal{A}\subseteq C(X)\rtimes_r\Gamma$ is simple for an inclusion $C(Y)\subset C(X)$ of minimal $\Gamma$-spaces whenever $C(Y)\rtimes_r\Gamma$ is simple. We shall also show that, for a large class of actions of $C^*$-simple groups $\Gamma\curvearrowright X$, including non-faithful action of any hyperbolic group with trivial amenable radical, every intermediate $C^*$-algebra $\mathcal{A}$, $C_r^*(\Gamma)\subset \mathcal{A}\subset C(X)\rtimes_r\Gamma$ is a crossed product of the form $C(Y)\rtimes_r\Gamma$, $C(Y)\subset C(X)$ is an inclusion of $\Gamma$-$C^*$-algebras.





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{\bfseries Please Note the Unusual Place!}
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