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$E$-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
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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

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