K-theory of non-commutative Bernoulli Shifts

2022/10/17 by Sayan Chakraborty, Siegfried Echterhoff, Chakraborty, Sayan +5
Mathematics · #19K35 (Primary) #46L80 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2210.09209

openalex publication_date 2022/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a large class of C*-algebras A, we calculate the K-theory of reduced crossed products A^{⊗ 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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