Skew-products of higher-rank graphs and crossed products by semigroups

Abstract

We consider a free action of an Ore semigroup on a higher-rank graph, and the induced action by endomorphisms of the $C^{\ast }$-algebra of the graph. We show that the crossed product by this action is stably isomorphic to the $C^{\ast }$-algebra of a quotient graph. Our main tool is Laca's dilation theory for endomorphic actions of Ore semigroups on $C^{\ast }$-algebras, which embeds such an action in an automorphic action of the enveloping group on a larger $C^{\ast }$-algebra.

14 pages. Accepted by Semigroup Forum

References in corpus (1)

• Simplicity of C*-algebras associated to higher-rank graphs

Cited by in corpus (1)

• On the K-theory of twisted higher-rank-graph C*-algebras