KK-lifting problem for dimension drop interval algebras
Georege A. Elliott, Zhiqiang Li
TL;DR
This paper studies the KK-lifting problem for generalized dimension drop interval algebras, revealing that some KK-elements preserve order structures but cannot be lifted to algebra homomorphisms, highlighting limitations in the lifting process.
Contribution
It identifies specific KK-elements that preserve order but cannot be lifted, advancing understanding of the KK-lifting problem for these algebras.
Findings
Existence of KK-elements preserving order but not liftable to homomorphisms.
Demonstration of limitations in KK-lifting for generalized dimension drop interval algebras.
Insight into the structure of KK-theory and order preservation in this context.
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.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology