Yet another description of the Connes-Higson functor. (English. Russian original) Zbl 1442.19015
Math. Notes 107, No. 4, 628-638 (2020); translation from Mat. Zametki 107, No. 4, 561-574 (2020).
Let \(A\) and \(B\) be \(C^*\)-algebras and let \(\mathfrak{A}(B)=C_b([0,\infty);B)/C_0([0,\infty);B)\) be the asymptotic \(C^*\)-algebra of \(B\).
An endofunctor \(\mathfrak{M}\) in the category of \(C^*\)-algebras is constructed and a set of special homotopy classes of \(*\)-homomorphisms from \(A\) to \(\mathfrak{M}(\mathfrak{A}(B))\) is defined so that this set endowed with the natural structure of an abelian group coincides with the group \(E_1(A, B)\) of A. Connes and N. Higson [C. R. Acad. Sci., Paris, Sér. I 311, No. 2, 101–106 (1990; Zbl 0717.46062)].
Reviewer: Vladimir M. Manuilov (Moskva)
MSC:
| 19K35 | Kasparov theory (\(KK\)-theory) |
| 46L80 | \(K\)-theory and operator algebras (including cyclic theory) |
| 46M15 | Categories, functors in functional analysis |
| 46L85 | Noncommutative topology |
Citations:
Zbl 0717.46062References:
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