On Asymptotic Homomorphisms into Calkin Algebras
Copyright policy )On Asymptotic Homomorphisms into Calkin Algebras
The paper is devoted to the classification problem for extensions of \(C^*\)-algebras. Earlier, \textit{G. G. Kasparov} has shown that extensions of nuclear \(C^*\)-algebras can be described in terms of the \(KK\)-functor [Izv. Akad. Nauk USSR, Ser. Mat. 44, 571-636 (1980; Zbl 0448.46051)]. In the general case, a similar description is unknown. In the present paper, the author defines so-called phantom extensions and for the case in which the \(C^*\)-algebra \(A\) is a second suspension, describes its extensions in terms of the \(E\)-theory of \textit{A. Connes} and \textit{N. Higson} [C. R. Acad. Sci., Paris, Sér. I 311, 101-106 (1990; Zbl 0717.46062)] and the group of phantom extensions.
- Lomonosov Moscow State University Russian Federation
phantom extension, \(C^*\)-algebras, \(K\)-theory and operator algebras (including cyclic theory), \(E\)-theory, Kasparov theory (\(KK\)-theory), Connes-Higson construction
phantom extension, \(C^*\)-algebras, \(K\)-theory and operator algebras (including cyclic theory), \(E\)-theory, Kasparov theory (\(KK\)-theory), Connes-Higson construction
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