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

2012/03/22 by Maloney, Ben, Pask, David, Raeburn, Iain · 1 citation
#20M20 #46L55 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1203.4860

Abstract

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

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