Crossed products of UHF algebras by some amenable groups
P. Nathanial · Hokkaido Mathematical Journal · 2000
Let A be a UHF C^{*} -algebra.It is shown that for every homo morphism \alpha : \mathbb{Z}^{n}arrow Aut(A) there exists an AF embedding \rho : A\aleph_{\alpha}\mathbb{Z}^{n}\sim>B such that \rho_{*} : K_{0} (A x_{\alpha}\mathbb{Z}^{n} ) arrow K_{0}(B) is also injective.Using Green's imprimitivity theorem it will follow that if A is UHF and \alpha : Garrow Aut(A) is a homomorphism then A n_{\alpha}G is always quasidiagonal for a large class of amenable groups including all extensions of discrete abelian groups by compact (not necessarily discrete or abelian) groups.