
TL;DR
This paper develops a theory of amenability for Fell bundles over discrete groups, introduces an approximation property as a sufficient condition for amenability, and applies it to graded C*-algebras and Cuntz-Krieger algebras.
Contribution
It formulates an approximation property for Fell bundles, proves its sufficiency for amenability, and applies the theory to graded C*-algebras and Cuntz-Krieger algebras.
Findings
The approximation property ensures amenability of Fell bundles.
All graded C*-algebras with a conditional expectation are isomorphic to their reduced cross-sectional algebra when the bundle is amenable.
The Cuntz-Krieger bundle is amenable for all {0,1}-entry matrices, regardless of property (I).
Abstract
Given a Fell bundle , over a discrete group , we construct its reduced cross sectional algebra , in analogy with the reduced crossed products defined for C*-dynamical systems. When the reduced and full cross sectional algebras of are isomorphic, we say that the bundle is amenable. We then formulate an approximation property which we prove to be a sufficient condition for amenability. A theory of -graded C*-algebras possessing a conditional expectation is developed, with an eye on the Fell bundle that one naturally associates to the grading. We show, for instance, that all such algebras are isomorphic to , when the bundle is amenable. We also study induced ideals in graded C*-algebras and obtain a generalization of results of Stratila and Voiculescu on AF-algebras, and of Nica on quasi-lattice ordered groups. A brief comment is made on…
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Mathematics and Applications · Point processes and geometric inequalities
