Journal of Operator Theory

Volume 42, Issue 1, Summer 1999 pp. 3-36.

${\bbb Z}/2{\bbb Z}$ -graded KK-theory and its relation with the graded Ext-functor

Authors: Ulrich Haag
Author institution: Inst. fur Reine Mathematik, Humboldt Universitat Berlin, Ziegelstr. 13A, 10099 Berlin, Germany

Summary: This paper studies the relation between

${\rm KK}$ -theory and the

${\rm Ext}$ -functor of Kasparov for

${\bbb Z}_2$ -grade d

$C^*$ -algebras. We use an approach similar to the picture of J. Cuntz in the ungraded case. We show that the graded

${\rm Ext}$ -functor coincides with

${\bbb Z}_2$ -equivariant

${\rm KK}$ -theory up to a shift in dimen sion and that the graded

${\rm KK}$ -functor can be expressed in terms of

${\bbb Z}_2$ -equ ivariant

${\rm KK}$ -theory. We derive a (double) exact sequence relating both theories.

Contents Full-Text PDF