On an intermediate bivariant theory for $C^*$-algebras, I

Constantin Dorin Dumitraşcu

paper

On an intermediate bivariant theory for $C^{*}$ -algebras, I

arXiv:math/0211160

Abstract

We construct a new bivariant theory, that we call $K E$ -theory, which is intermediate between the $K K$ -theory of G. G. Kasparov, and the $E$ -theory of A. Connes and N. Higson. For each pair of separable graded $C^{*}$ -algebras $A$ and $B$ , acted upon by a locally compact $σ$ -compact group $G$ , we define an abelian group $K E_{G} (A, B)$ . We show that there is an associative product $K E_{G} (A, D) \otimes K E_{G} (D, B) \to K E_{G} (A, B)$ . Various functoriality properties of the $K E$ -theory groups and of the product are presented. The new theory has a simpler product than $K K$ -theory and there are natural transformations $K K_{G} \to K E_{G}$ and $K E_{G} \to E_{G}$ . The complete description of these maps will form the substance of a second paper.

44 pages

Cited by in corpus (1)

Group actions on Smale space C*-algebras

On an intermediate bivariant theory for C∗-algebras, I

Abstract

Cited by in corpus (1)

On an intermediate bivariant theory for $C^{*}$ -algebras, I