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The group of unital $C^*$-extensions

Vladimir Manuilov·Klaus Thomsen
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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 The six-terms exact sequence is an unpublished result of G. Skandalis.

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Vladimir Manuilov, Klaus Thomsen. 2005-01-26. The group of unital $C^*$-extensions. https://arxiv.org/abs/math/0501472

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