Extensions by Simple C * -Algebras: Quasidiagonal Extensions

Source abstract

Abstract Let A be an amenable separable C * -algebra and B be a non-unital but σ-unital simple C * - algebra with continuous scale. We show that two essential extensions τ 1 and τ 2 of A by B are approximately unitarily equivalent if and only if If A is assumed to satisfy the Universal Coefficient Theorem, there is a bijection fromapproximate unitary equivalence classes of the abovementioned extensions to KL ( A , M ( B )/ B ). Using KL ( A , M ( B )/ B ), we compute exactly when an essential extension is quasidiagonal. We show that quasidiagonal extensions may not be approximately trivial. We also study the approximately trivial extensions.