K-theory of noncommutative Bernoulli shifts

Authors

Sayan Chakraborty, Indian Statistical Institute, Kolkata
Siegfried Echterhoff, University of Münster
Julian Kranz, University of Münster
Shintaro Nishikawa, University of Münster

Article Type

Research Article

Publication Title

Mathematische Annalen

Abstract

For a large class of C^∗-algebras A, we calculate the K-theory of reduced crossed products A^⊗G⋊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≀G for large classes of groups H and G. Our methods use a generalization of techniques developed by the second named author together with Joachim Cuntz and Xin Li, and a trivialization theorem for finite group actions on UHF algebras developed in a companion paper by the third and fourth named authors.

First Page

2671

Last Page

2703

DOI

10.1007/s00208-023-02587-w

Publication Date

1-1-2024

Comments

Open Access; Hybrid Gold Open Access

Recommended Citation

Chakraborty, Sayan; Echterhoff, Siegfried; Kranz, Julian; and Nishikawa, Shintaro, "K-theory of noncommutative Bernoulli shifts" (2024). Journal Articles. 4872.
https://digitalcommons.isical.ac.in/journal-articles/4872