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arXiv · 1609.00604

Deformations of Wreath Products

Marius Dadarlat·Ulrich Pennig·Andrew Schneider
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Abstract

Connectivity is a homotopy invariant property of a separable C*-algebra A which has three important consequences: absence of nontrivial projections, quasidiagonality and realization of the Kasparov group KK(A,B) as homotopy classes of asymptotic morphisms from A to the stabilization of B if A is nuclear. Here we give a new characterization of connectivity for separable exact C*-algebras and use this characterization to show that the class of discrete countable amenable groups whose augmentation ideals are connective is closed under generalized wreath products. In a related circle of ideas, we give a result on quasidiagonality of reduced crossed-product C*-algebras associated to noncommutative Bernoulli actions.

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Marius Dadarlat, Ulrich Pennig, Andrew Schneider. 2016-09-02. Deformations of Wreath Products. https://doi.org/10.1112/blms.12008

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