Classification of Extensions of Classifiable C*-algebras

Abstract

We classify extensions of certain classifiable C*-algebras using the six term exact sequence in K-theory together with the positive cone of the K_0-groups of the distinguished ideal and quotient. We then apply our results to a class of C*-algebras arising from substitutional shift spaces.

22 pages, Reordered some sections, an application involving graph algebras is added

References in corpus (3)

• Symbolic Dynamics, Partial Dynamical Systems, Boolean Algebras and C*-algebras Generated by Partial Isometries
• Lifting KK-elements, asymptotical unitary equivalence and classification of simple C*-algebras
• A classification theorem for direct limits of extensions of circle algebras by purely infinite C*-algebras

Cited by in corpus (8)

• Classifying $C^{\ast }$-algebras with both finite and infinite subquotients
• The ordered K-theory of a full extension
• Strong classification of purely infinite Cuntz-Krieger algebras
• Classification of graph C*-algebras with no more than four primitive ideals
• The extension problem for graph $C^{\ast }$-algebras
• Corrigendum to "Classifying C*-algebras with both finite and infinite subquotients"
• Sturmian subshifts and their C*-algebras
• Constructing number field isomorphisms from *-isomorphisms of certain crossed product C*-algebras