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Journal of Operator Theory

Volume 91, Issue 1, Winter 2024  pp. 125-168.

Extensions of quasidiagonal $C^*$-algebras and controlling the $K_0$-map of embeddings

Authors:  Iason Moutzouris
Author institution: Department of Mathematics, Purdue University, West Lafayette, IN 47907, U.S.A.

Summary:  We study the validity of the Blackadar-Kirchberg conjecture for extensions of separable, nuclear, quasidiagonal $C^*$-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 $C^*$-algebras that is closed under local approximations and contains all separable ASH-algebras, as well as certain classes of simple, unital $C^*$-algebras and crossed products of unital $C^*$-algebras with $\mathbb{Z}$.

Keywords:  $C^*$-algebras, extensions, quasidiagonality, Blackadar-Kirchberg Conjecture, {\rm ASH}-algebras

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