Semi-invertible extensions and asymptotic homomorphisms

2003/10/31 by Vladimir Manuilov, V. Manuilov, K. Thomsen +3
Mathematics · #19K33 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.OA #msc:19K33

paper · pdf · doi:10.48550/arxiv.math/0310491

31 pages, LaTeX, XYpic

arxiv created 2003/10/31 · openalex publication_date 2003/10/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the semigroup Ext(A,B) of extensions of a separable C*-algebra A by a stable C*-algebra B modulo unitary equivalence and modulo asymptotically split extensions. This semigroup contains the group Ext^-1/2(A,B) of invertible elements (i.e. of semi-invertible extensions). We show that the functor Ext^1/2(A,B) is homotopy invariant and that it coincides with the functor of homotopy classes of asymptotic homomorphisms from C(\mathbb T)⊗ A to M(B) that map SA⊆ C(\mathbb T)⊗ A into B.

Related

• Asymptotically split extensions and E-theory
• Extensions of C*-algebras and translation invariant asymptotic homomorphisms
• The Connes-Higson construction is an isomorphism
• Asymptotic homomorphisms into the Calkin algebra
• Semi-invertible extensions of C*-algebras