Strongly graded groupoid and directed graph algebras

Abstract

We show the reduced $C^{\ast }$-algebra of a graded ample groupoid is a strongly graded $C^{\ast }$-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 $C^{\ast }$-algebra of an arbitrary graph.

In this version, minor corrections were made and references were added

References in corpus (1)

• Groupoid algebras as covariance algebras