Deformations of Wreath Products

TL;DR

This paper characterizes connectivity in separable exact C*-algebras and explores its stability under wreath products, also examining quasidiagonality of certain crossed-product C*-algebras.

Contribution

It provides a new characterization of connectivity for separable exact C*-algebras and shows closure under wreath products, also analyzing quasidiagonality in noncommutative Bernoulli actions.

Findings

Connectivity characterized for separable exact C*-algebras.

Closure of amenable groups with connective augmentation ideals under wreath products.

Quasidiagonality results for reduced crossed-product C*-algebras.

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.