Hostname: page-component-76fb5796d-25wd4 Total loading time: 0 Render date: 2024-04-26T08:57:04.363Z Has data issue: false hasContentIssue false
  • English
  • Français

$E$-Theory is a Special Case of $KK$-Theory

Published online by Cambridge University Press:  08 March 2004

V. Manuilov  and
K. Thomsen
V. Manuilov
Affiliation:
Mechanics and Mathematics Department, Moscow State University, 119899 Moscow, Russia. E-mail: manuilov@higeom.math.msu.su
K. Thomsen
Affiliation:
Institute of Mathematical Sciences, Aarhus University, Ny Munkegade, 8000 Aarhus C, Denmark. E-mail: matkt@imf.au.dk
Get access

Abstract

Let $A$ and $B$ be C*-algebras, with $A$ separable and $B$$\sigma$-unital and stable. It is shown that there are natural isomorphisms

$$ E(A,B) = KK(SA,Q(B)) = [SA,Q(B) \otimes K], $$

where $SA=C_0(0, 1) \otimes A$, $[\cdot, \cdot]$ denotes the set of homotopy classes of *-homomorphisms, $Q(B) = M(B) / B$ is the generalized Calkin algebra, and $K$ denotes the C*-algebra of compact operators of an infinite-dimensional separable Hilbert space.

Keywords

KK-theoryE-theoryextensions of C*-algebras19K3519K3346M15
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 88 , Issue 2 , March 2004 , pp. 455 - 478
Copyright
2004 London Mathematical Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)