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

Abstract

Let $C^{\ast }$-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 $C^{\ast }$-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 $C^{\ast }$-algebras.

37 pages

References in corpus (5)

• Continuous orbit equivalence of topological Markov shifts and Cuntz-Krieger algebras
• Equivalence and stable isomorphism of groupoids, and diagonal-preserving stable isomorphisms of graph C*-algebras and Leavitt path algebras
• Reconstruction of groupoids and C*-rigidity of dynamical systems
• Étale groupoids and their $C^{\ast }$-algebras
• $\ast$-isomorphism of Leavitt path algebras over $\mathbb{Z}$

Cited by in corpus (4)

• A uniqueness theorem for twisted groupoid C*-algebras
• Alexandrov groupoids and the nuclear dimension of twisted groupoid ${\mathrm{C}}^{\ast }$-algebras
• Normalizers and Approximate Units for Inclusions of C*-Algebras
• Analyzing the Weyl construction for dynamical Cartan subalgebras