KK-lifting problem for dimension drop interval algebras

2013/06/16 by Georege A. Elliott, Zhiqiang Li, Elliott, Georege A. +1
Mathematics · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Operator Algebras (math.OA) #math.OA

paper · pdf · doi:10.48550/arxiv.1306.3623

26 pages

arxiv created 2013/06/16 · openalex publication_date 2013/06/16 · arxiv updated 2013/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the KK-lifting problem for generalized dimension drop interval algebras (with possibly different dimension drops at the endpoints). It turns out that there exist KK-elements between two such algebras which preserve the Dadarlat-Loring order structure on K-theory with coefficient, but fail to be lifted to a homomorphism between the algebras.

Related

• On the classification of C*-algebras of real rank zero, V
• On the Decomposition Theorems for C*-algebras
• A note on C^*-algebras with Lifting Property
• Lifting Lie algebras over the residue field of a discrete valuation ring
• Lifting via cocycle deformation