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Graded C*-algebras and twisted groupoid C*-algebras (1909.04710v1)

Published 10 Sep 2019 in math.OA

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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