Crossed products of UHF algebras by some amenable groups

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Abstract

Let A be a UHF C*-algebra. It is shown that for every homo morphism α:Zn⟶ Aut(A) there exists an AF embedding ρ: A ⋊ρZn⟶B such that ρ*:K0(A ⋊ρZn⟶K0(B) is also injective. Using Green’s imprimitivity theorem it will follow that if A is UHF and α: G ⟶ Aut(A) is a homomorphism then A ⋊ρG is always quasidiagonal for a large class of amenable groupsincluding all extensions of discrete abelian groups by compact (not necessarily discrete or abelian) groups.

Original languageEnglish (US)
Pages (from-to)201-211
Number of pages11
JournalHokkaido Mathematical Journal
Volume29
Issue number1
DOIs
Publication statusPublished - Jan 1 2000

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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