2022/09/30 by Julian Kranz, Kranz, Julian, Shintaro Nishikawa +1
Mathematics · #19K35 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA) #Primary 46L80 #Secondary 20C05
paper · pdf · doi:10.48550/arxiv.2210.00061
openalex publication_date 2022/09/30 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
Building on Enders--Schemeitat--Tikuisis' classification, we show that a separable C^*-algebra A with approximately inner flip in the UCT class is K-theoretically self-absorbing if and only if for every finite group G, the Bernoulli shift on A⊗ G is KKG-equivalent to the trivial action. This in particular applies to UHF-algebras of infinite type and computes the K-theory of the associated crossed product. Along the way, we obtain an alternative proof of Hirshberg--Winter's result that the Bernoulli shift of G on a UHF-algebra of infinite type absorbs the trivial action up to conjugacy. For more general amenable groups G, we develop K-theory formulas for Bernoulli shifts on UHF-absorbing C^*-algebras, and establish KKG-triviality for Bernoulli shifts on strongly self-absorbing C^*-algebras satisfying the UCT.