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arXiv · 1909.04710

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

Jonathan Brown·Adam Fuller·David Pitts·Sarah Reznikoff
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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.

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Jonathan Brown, Adam Fuller, David Pitts, Sarah Reznikoff. 2019-09-10. Graded C*-algebras and twisted groupoid C*-algebras. https://arxiv.org/abs/1909.04710

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