Nuclearity and exactness for groupoid crossed products
نویسندگان
چکیده
منابع مشابه
Nuclearity and Exactness for Groupoid Crossed Product C∗-algebras
The focus of this thesis is the study of nuclearity and exactness for groupoid crossed product C∗-algebras. In particular, we present generalizations of two well-known facts from group dynamical systems and crossed products to the groupoid setting. First, we show that if G is an amenable groupoid acting on an upper-semicontinuous C∗-bundle A with nuclear section algebra A, then the associated g...
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We define the notion of a principal S-bundle where S is a groupoid group bundle and show that there is a one-to-one correspondence between principal S-bundles and elements of a sheaf cohomology group associated to S. We also define the notion of a locally unitary action and show that the spectrum of the crossed product is a principal b S-bundle. Furthermore, we prove that the isomorphism class ...
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Suppose that G is a groupoid acting on a small category H in the sense of [9, Definition 4] and H ×α G is the resulting semi-direct product category (as in [9, Proposition 8]). We show that there exists a subcategory Hr ⊆ H satisfying some nice property called “regularity” such that Hr ×α G = H ×α G. Moreover, we show that there exists a so-called “quasi action” (see Definition 3.1) β of G on C...
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Given a labeling c of the edges of a directed graph E by elements of a discrete group G, one can form a skew-product graph E ×c G. We show, using the universal properties of the various constructions involved, that there is a coaction δ of G on C∗(E) such that C∗(E ×c G) is isomorphic to the crossed product C ∗(E) ×δ G. This isomorphism is equivariant for the dual action δ̂ and a natural action ...
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ژورنال
عنوان ژورنال: Journal of Operator Theory
سال: 2015
ISSN: 0379-4024,1841-7744
DOI: 10.7900/jot.2014jun06.2032