Graded C*-algebras and twisted groupoid C*-algebras

2019/09/10 by Jonathan H. Brown, Adam H. Fuller, Brown, Jonathan +5 · 3 citations
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1909.04710

openalex publication_date 2019/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let C^*-algebra that is acted upon by a compact abelian group. We show that if the fixed-point algebra of the action contains a Cartan subalgebra D satisfying an appropriate regularity condition, then A is the reduced C^*-algebra of a groupoid twist. We further show that the embedding D \hookrightarrow A is uniquely determined by the twist. These results generalize Renault's results on Cartan subalgebras of C^*-algebras.

Citations

• Étale groupoids and their C^*-algebras

Cited by

• On Diagonal bimodules of étale groupoid C^*-algebras
• Generalised Twisted Groupoids and their C*-algebras
• On Graded Quasi-Cartan Pairs and Twisted Steinberg Algebras

Related

• Cartan semigroups and twisted groupoid C*-algebras
• Generalised Twisted Groupoids and their C*-algebras
• The C*-algebra of a twisted groupoid extension
• Essential Cartan subalgebras of C^*-algebras
• Nontraditional models of Γ-Cartan pairs