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

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

2012-03-22

arxiv.org/abs/1203.4860v1

Mathematics

Operator Algebras

14 pages

Scientific paper

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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