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arXiv · 2210.09209

$K$-theory of non-commutative Bernoulli Shifts

Sayan Chakraborty·Siegfried Echterhoff·Julian Kranz·Shintaro Nishikawa
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Abstract

For a large class of 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 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.

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BibTeXRIS

Sayan Chakraborty, Siegfried Echterhoff, Julian Kranz, Shintaro Nishikawa. 2022-10-17. $K$-theory of non-commutative Bernoulli Shifts. https://arxiv.org/abs/2210.09209

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