Deformations of Wreath Products
Operator Algebras
2023-11-27 v1 K-Theory and Homology
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.
Keywords
Cite
@article{arxiv.1609.00604,
title = {Deformations of Wreath Products},
author = {Marius Dadarlat and Ulrich Pennig and Andrew Schneider},
journal= {arXiv preprint arXiv:1609.00604},
year = {2023}
}