Connective C*-algebras

Abstract

Connectivity is a homotopy invariant property of separable C*-algebras which has three notable consequences: absence of nontrivial projections, quasidiagonality and a more geometric realization of KK-theory for nuclear C*-algebras using asymptotic morphisms. The purpose of this paper is to further explore the class of connective C*-algebras. We give new characterizations of connectivity for exact and for nuclear separable C*-algebras and show that an extension of connective separable nuclear C*-algebras is connective. We establish connectivity or lack of connectivity for C*-algebras associated to certain classes of groups: virtually abelian groups, linear connected nilpotent Lie groups and linear connected semisimple Lie groups.

26 pages. A glitch in Definition 2.9 is corrected

References in corpus (3)

• Describing the platycosms
• Deformations of Wreath Products
• Deformations of nilpotent groups and homotopy symmetric $C^{\ast }$-algebras

Cited by in corpus (3)

• AF-embeddability for Lie groups with $T_1$ primitive ideal spaces
• Inductive limits of semiprojective C*-algebras
• Examples of non connective C*-algebras