Strongly graded groupoid and directed graph algebras

Published 9 Mar 2020 in math.OA and math.RA | (2003.04443v2)

Abstract: We show the reduced $C^*$-algebra of a graded ample groupoid is a strongly graded $C^*$-algebra if and only if the corresponding Steinberg algebra is a strongly graded ring. We apply this result to get a theorem about the Leavitt path algebra and $C^*$-algebra of an arbitrary graph.

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