Geodesic
$KK$-theory as the $K$-theory of $C^*$-categories
Homology, homotopy, and applications, Tome 2 (2000) no. 1, pp. 127-145.

Voir la notice de l'article provenant de la source International Press of Boston

Let complex $C^{*}$ algebras be endowed with a norm-continuous action of a fixed compact second countable group. From a separable $C^{*}$-algebra $A$ and a $\sigma $-unital $C^{*}$-algebra $B$, we construct a $C^{*}$-category $\mathrm{Rep} (A,B)$ and an isomorphism \[ \kappa :K^{i+1}(\mathrm{Rep} (A,B))\rightarrow KK^i(A,B),\;\;\;i\in \mathbb{Z}_2, \] where on the left-hand side are Karoubi's topological $K$-groups, and on the right-hand side are Kasparov’s equivariant bivariant $K$-groups.
DOI : 10.4310/HHA.2000.v2.n1.a10
Classification : 19J99, 19K35, 46L89, 46Mxx
Keywords: $K$-theory, $KK$-theory, $C^*$-category 
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     author = {Tamaz Kandelaki},
     title = {$KK$-theory as the $K$-theory of $C^*$-categories},
     journal = {Homology, homotopy, and applications},
     pages = {127--145},
     publisher = {mathdoc},
     volume = {2},
     number = {1},
     year = {2000},
     doi = {10.4310/HHA.2000.v2.n1.a10},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2000.v2.n1.a10/}
}
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Tamaz Kandelaki. $KK$-theory as the $K$-theory of $C^*$-categories. Homology, homotopy, and applications, Tome 2 (2000) no. 1, pp. 127-145. doi : 10.4310/HHA.2000.v2.n1.a10. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2000.v2.n1.a10/

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