ON ℤ/2ℤ-GRADED KK-THEORY AND ITS RELATION WITH THE GRADED Ext-FUNCTOR

ON ℤ/2ℤ-GRADED KK-THEORY AND ITS RELATION WITH THE GRADED Ext-FUNCTOR

This paper studies the relation between KK-theory and the Ext-functor of Kasparov for ℤ2-graded C*-algebras. We use an approach similar to the picture of J. Cuntz in the ungraded case. We show that the graded Ext-functor coincides with ℤ2-equivariant KK-theory up to a shift in dimension and that the...

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Veröffentlicht in:Journal of operator theory 1999-07, Vol.42 (1), p.3-36
1. Verfasser: HAAG, ULRICH
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Automorphisms
Homomorphisms
Mathematical theorems
Morphisms
Subalgebras
Tensors
Universal algebra
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Zusammenfassung:This paper studies the relation between KK-theory and the Ext-functor of Kasparov for ℤ2-graded C*-algebras. We use an approach similar to the picture of J. Cuntz in the ungraded case. We show that the graded Ext-functor coincides with ℤ2-equivariant KK-theory up to a shift in dimension and that the graded KK-functor can be expressed in terms of ℤ2-equivariant KK-theory. We derive a (double) exact sequence relating both theories.
ISSN:0379-4024
1841-7744