Some classifiable groupoid C*-algebras with prescribed K-theory

Abstract

Given a simple, acyclic dimension group $G_0$ and countable, torsion-free, abelian group $G_1$, we construct a minimal, amenable, étale equivalence relation $R$ on a Cantor set whose associated groupoid $C^{\ast }$-algebra, $C^{\ast }(R)$, is tracially AF, and hence classifiable in the Elliott classification scheme for simple, amenable, separable $C^{\ast }$-algebras, and with $K_{\ast }(C^{\ast }(R))\cong (G_0,G_1)$.

34 pages, to appear Math. Ann

Cited by in corpus (2)

• Cartan subalgebras and the UCT problem, II
• Groupoid Models of $C^{\ast }$-algebras and Gelfand Duality