The group of unital $C^*$-extensions

Abstract

Let $A$ and $B$ be separable $C^*$-algebras, $A$ unital and $B$ stable. It is shown that there is a natural six-terms exact sequence which relates the group which arises by considering all semi-split extensions of $A$ by $B$ to the group which arises by restricting the attention to \emph{unital} semi-split extensions of $A$ by $B$. The six-terms exact sequence is an unpublished result of G. Skandalis.