Extensions of quasidiagonal $C^{\ast }$-algebras and controlling the $K_0$-map of embeddings

Abstract

We study the validity of the Blackadar-Kirchberg conjecture for extensions of separable, nuclear, quasidiagonal $C^{\ast }$-algebras that satisfy the UCT. More specifically, we show that the conjecture for the extension has an affirmative answer if the ideal lies in a class of $C^{\ast }$-algebras that is closed under local approximations and contains all separable ASH algebras, as well as certain classes of simple, unital $C^{\ast }$-algebras and crossed products of unital $C^{\ast }$-algebras with the integers.

arXiv comment36 pages, revision based on referree's comments. To appear in the Journal of Operator Theory