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

2016/11/15 by Ian F. Putnam, Putnam, Ian F. · 2 citations
Mathematics · #46L35 #46L80 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L35 #msc:46L80

paper · pdf · doi:10.48550/arxiv.1611.04649

34 pages, to appear Math. Ann

openalex publication_date 2016/11/15 · arxiv created 2017/09/25 · arxiv updated 2017/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a simple, acyclic dimension group G₀ and countable, torsion-free, abelian group G₁, we construct a minimal, amenable, étale equivalence relation R on a Cantor set whose associated groupoid C^*-algebra, C^*(R), is tracially AF, and hence classifiable in the Elliott classification scheme for simple, amenable, separable C^*-algebras, and with K_*(C^*(R)) ≅(G₀, G₁).

Cited by

• Cartan subalgebras and the UCT problem, II
• Etale equivalence relations with certain prescribed torsion in their homology

Related

• Almost elementary groupoid models for C^*-algebras
• Classifiable C^*-algebras from minimal ℤ-actions and their orbit-breaking subalgebras
• Simplicity criteria for etale groupoid C^*-algebras
• Simplicity of algebras associated to étale groupoids
• Isomorphisms in K-theory from isomorphisms in groupoid homology theories