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) - in das SS 2024 verschoben

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 $H\wr G$ 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.

In das SS 2024 verschoben.