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arXiv · 1609.09453

Connective C*-algebras

Marius Dadarlat·Ulrich Pennig
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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.

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Marius Dadarlat, Ulrich Pennig. 2016-09-29. Connective C*-algebras. https://doi.org/10.1016/j.jfa.2017.02.009

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