IMSc Webinar

On the Existence, or lack, of non-commutative factors of a dynamical system

Tattwamasi Amrutam

Ben Gurion University

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zoom.us/j/91820411106

Meeting ID: 918 2041 1106
Passcode: Vaughan


Let X be a compact Hausdorff \Gamma-space. We
say that the corresponding crossed-product C^*-algebra
C(X)\rtimes_r\Gamma] is reflecting when every intermediate C^*
-algebra C_r^*(\Gamma)\subset\mathcal{A}\subset C(X)\rtimes_r\Gamma,
which we consider a“ non-commutative factor”, is of the form
\mathcal{A}=C(Y)\rtimes_r\Gamma], corresponding to a dynamical factor
X\to Y. We establish (dynamical) sufficient conditions on (X,
\Gamma) under which C(X)\rtimes \Gamma is reflecting, and provide several
examples where these sufficient conditions apply. It turns out that when
our conditions are satisfied, the acting group \Gamma is
necessarily C^*-simple. In the second part of the talk, we will
examine the opposite aspect of the story, when \Gamma is not
C^*-simple. This talk is based on two recent joint works with Eli Glasner
and Yair Glasner.