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

2002/11/10 by Constantin Dorin Dumitraşcu, Constantin Dorin Dumitrașcu, Dumitraşcu, Constantin Dorin · 2 citations
Mathematics · Physics and Astronomy · #19K35 #46L80 #46L85 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #math.OA #msc:19K35 #msc:46L80 #msc:46L85

paper · pdf · doi:10.48550/arxiv.math/0211160

44 pages

arxiv created 2002/11/10 · openalex publication_date 2002/11/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a new bivariant theory, that we call KE-theory, which is intermediate between the KK-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 KE_G(A,B). We show that there is an associative product KE_G(A,D) ⊗ KE_G(D,B) → KE_G(A,B). Various functoriality properties of the KE-theory groups and of the product are presented. The new theory has a simpler product than KK-theory and there are natural transformations KK_G → KE_G and KE_G → E_G. The complete description of these maps will form the substance of a second paper.

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• The odd spectral localiser via asymptotic morphisms and quasi-projections
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