AG Lie-Gruppen: S. Echterhoff, Universität Münster: K-Theory for Crossed Products by Bernoulli Shifts (Joint work with Sayan Chakraborty, Julian Kranz and Shintaro Nishikawa)

Date: 03-06-2024Time: 2:15 PM – 3:45 PMLocation: Übungsraum Ü2, Cauerstr. 11, Erlangen

K-Theory for Crossed Products by Bernoulli Shifts (Joint work with Sayan Chakraborty, Julian Kranz and Shintaro Nishikawa) - Vortragender: Siegfried Echterhoff, Universität Münster – Einladender: Kang Li

Abstract: For a large class of unital $C^*$-algebras $A$, we calculate the $K$-theory of reduced crossed products $A^{otimes G}rtimes_rG$ of Bernoulli shifts by groups satisfying the Baum--Connes conjecture. In particular, we give explicit formulas for finite-dimensional $C^*$-algebras, UHF-algebras, rotation algebras, and several other examples. As an application, we obtain a formula for the $K$-theory of reduced $C^*$-algebras of wreath products $Hwr G$ for large classes of groups $H$ and $G$. Our results are motivated and generalize earlier results of Xin Li about the K-theory of lamplighter groups.

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Event Details

Date:
03-06-2024
Time:
2:15 PM – 3:45 PM
Location:

Übungsraum Ü2, Cauerstr. 11, Erlangen

Event Categories:
LIE-Gruppen