E-theory is a special case of KK-theory

2002/09/09 by Vladimir Manuilov, Klaus Thomsen, Manuilov, Vladimir +1
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA) #math.OA

paper · pdf · doi:10.48550/arxiv.math/0209088

22 pages, LaTeX

arxiv created 2002/09/09 · openalex publication_date 2002/09/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A and B be C^*-algebras, A separable, and B σ-unital and stable. It is shown that there are natural isomorphisms E(A,B)=KK(SA,Q(B))=[SA,Q(B)⊗ K], where SA=C₀(0,1)⊗ A, [⋅,⋅] 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.

Related

• A KK-like picture for E-theory of C*-algebras
• On an intermediate bivariant theory for C^*-algebras, I
• Some remarks in C^*- and K-theory
• Nonstable K--theory for extension algebras of the simple purely infinite C^*--algebra by certain C^*--algebras
• E-theory for C^∗-Categories