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Social and Behavioral Sciences Commons™
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Full-Text Articles in Social and Behavioral Sciences
Skew-Products Of Higher-Rank Graphs And Crossed Products By Semigroups, Benjamin Maloney, David Pask, Iain Raeburn
Skew-Products Of Higher-Rank Graphs And Crossed Products By Semigroups, Benjamin Maloney, David Pask, Iain Raeburn
Faculty of Engineering and Information Sciences - Papers: Part A
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.
Purely Infinite Partial Crossed Products, Thierry Giordano, Adam Sierakowski
Purely Infinite Partial Crossed Products, Thierry Giordano, Adam Sierakowski
Faculty of Engineering and Information Sciences - Papers: Part A
Let (A, G, alpha) be a partial dynamical system. We show that there is a bijective corespondence between G-invariant ideals of A and ideals in the partial crossed prroduct A xalpha, r G provided the action is exact and residually topologically free.