The group of unital \(C^*\)-extensions. (English) Zbl 1119.46041
Bojarski, Bogdan (ed.) et al., \(C^*\)-algebras and elliptic theory. Basically formed by contributions from the international conference, Bȩdlewo, Poland, February 2004. In cooperation with Dan Burghelea, Richard Melrose and Victor Nistor. Basel: Birkhäuser (ISBN 3-7643-7686-4/hbk). Trends in Mathematics, 151-156 (2006).
Summary: 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 unital semi-split extensions of \(A\) by \(B\). The six-terms exact sequence is an unpublished result of G. Skandalis.
For the entire collection see [Zbl 1097.58001].
For the entire collection see [Zbl 1097.58001].
MSC:
| 46L05 | General theory of \(C^*\)-algebras |
| 46L80 | \(K\)-theory and operator algebras (including cyclic theory) |
| 19K35 | Kasparov theory (\(KK\)-theory) |
| 19K33 | Ext and \(K\)-homology |
