Mathematics Colloquium

Speaker: 
Professor Jan Cameron, Vassar College

An ongoing thread of research in operator algebras investigates the structure of \emph{intermediate subalgebras} for inclusions $B \subseteq A$ of C$^*$-algebras, that is, algebras $D$ satisfying $B \subseteq D \subseteq A.$  Of particular interest is the reduced crossed product construction, which associates a C$^*$-algebra $A \rtimes_{\alpha,r} G$ to the action of a discrete group $G$ on a unital C$^*$-algebra $A$.  In this setting, any subgroup $H$ of $G$ generates a C$^*$-subalgebra  $A \rtimes_{\alpha,r} H$ lying between $A$ and  $A \rtimes_{\alpha,r} G$.  Are these all of the intermediate subalgebras?  If so, it is said that a \emph{Galois correspondence} holds for the inclusion $A \subseteq A \rtimes_{\alpha,r} G$.  When $A$ is unital and simple and the action is outer,  a Galois correspondence was established for crossed products by abelian groups by Landstad, Olesen, and Pedersen; and for crossed products by finite groups, by Izumi.  My recent joint work with Roger Smith generalized these results to crossed products by arbitrary discrete groups.  In this talk, I will discuss our recent work on this problem, and survey some current research and related questions for C$^*$-algebras and von Neumann algebras.

 

*Recordings of the Zoom Session will be available a few hours later in this folder (https://uicapture.hosted.panopto.com/Panopto/Pages/Sessions/List.aspx?folderID=b23b61cc-a48a-4de7-99fc-ae46015b8b6e ).  Find the date of the session you want to watch, and click the session title to watch the recording.

Event Date: 
April 28, 2022 - 3:30pm
Location: 
118 MLH and Online (see URL)
Calendar Category: 
Colloquium