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Social and Behavioral Sciences *Commons*^{™}

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## Full-Text Articles in Social and Behavioral Sciences

Realising The C*-Algebra Of A Higher-Rank Graph As An Exel's Crossed Product, Nathan Brownlowe

#### Realising The C*-Algebra Of A Higher-Rank Graph As An Exel's Crossed Product, Nathan Brownlowe

*Faculty of Engineering and Information Sciences - Papers: Part A*

We use the boundary-path space of a finitely-aligned k-graph Lambda to construct a compactly-aligned product system X, and we show that the graph algebra C*(Lambda) is isomorphic to the Cuntz-Nica-Pimsner algebra NO(X). In this setting, we introduce the notion of a crossed product by a semigroup of partial endomorphisms and partially-defined transfer operators by defining it to be NO(X). We then compare this crossed product with other definitions in the literature.

Purely Infinite C-Algebras Arising From Crossed Products, Mikael Rordam, Adam Sierakowski

#### Purely Infinite C-Algebras Arising From Crossed Products, Mikael Rordam, Adam Sierakowski

*Faculty of Engineering and Information Sciences - Papers: Part A*

We study conditions that will ensure that a crossed product of a C-algebra by a discrete exact group is purely infinite (simple or non-simple). We are particularly interested in the case of a discrete non-amenable exact group acting on a commutative C-algebra, where our sufficient conditions can be phrased in terms of paradoxicality of subsets of the spectrum of the abelian C-algebra. As an application of our results we show that every discrete countable non-amenable exact group admits a free amenable minimal action on the Cantor set such that the corresponding crossed product C-algebra is a Kirchberg algebra in the …