Nuclearity and Exactness for Groupoid Crossed Products

2014/06/06 by LaLonde, Scott M. · 2 citations
#46L06 #46L55 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1406.1749

Abstract

Let (A, G, α) be a groupoid dynamical system. We show that if G is assumed to be measurewise amenable and the section algebra A = Γ₀(G⁽⁰⁾, A) is nuclear, then the associated groupoid crossed product is also nuclear. This generalizes an earlier result of Green for crossed products by locally compact groups. We also extend a related result of Kirchberg to groupoids. In particular, if A is exact and G is amenable, then we show that A \rtimes G is exact.

Cited by

• Reduced C^*-algebras of Product Systems -- an E₀-semigroup and a Groupoid perspective
• Some remarks on Reduced C^*-algebras of semigroup dynamical systems and product systems

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