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This article is cited in 3 scientific papers (total in 3 papers)
Yet Another Description of the Connes–Higson Functor
G. S. Makeev Lomonosov Moscow State University
Abstract:
Suppose that $A$ and $B$ are $C^{*}$-algebras, $A$ is separable, and $B$ is stable. The elements of the group $E_{1}(A,B)$ in Connes–Higson $E$-theory are represented by $*$-homomorphisms from the suspension of $A$ to the asymptotic algebra $\mathfrak AB$. In the paper, an endofunctor $\mathfrak M$ in the category of $C^{*}$-algebras is constructed and a set of special homotopy classes of $*$-homomorphisms from $A$ to $\mathfrak{MA}B$ is defined so that this set endowed with the natural structure of an Abelian group coincides with $E_{1}(A,B)$.
Keywords:
$E$-theory, $KK$-theory, homotopy invariant functor.
Received: 04.02.2019 Revised: 10.06.2019
Citation:
G. S. Makeev, “Yet Another Description of the Connes–Higson Functor”, Mat. Zametki, 107:4 (2020), 561–574; Math. Notes, 107:4 (2020), 628–638
Linking options:
https://www.mathnet.ru/eng/mzm12336https://doi.org/10.4213/mzm12336 https://www.mathnet.ru/eng/mzm/v107/i4/p561
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Abstract page: | 240 | Full-text PDF : | 25 | References: | 28 | First page: | 12 |
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