Date/heure
11 avril 2024
14:15 - 15:15
Oratrice ou orateur
Siegfried Echterhoff (Münster)
Catégorie d'évènement Séminaire Théorie de Lie, Géométrie et Analyse
Résumé
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.
(joint work with Sayan Chakraborty, Julian Kranz, and Shintaro Nishikawa)