Spanier-Whitehead K-duality for $C^*$-algebras
Operator Algebras
2017-06-14 v4 Algebraic Topology
Abstract
Classical Spanier-Whitehead duality was introduced for the stable homotopy category of finite CW complexes. Here we provide a comprehensive treatment of a noncommutative version, termed Spanier-Whitehead -duality, which is defined on the category of -algebras whose -theory is finitely generated and that satisfy the UCT with morphisms the -groups. We explore what happens when these assumptions are relaxed in various ways. In particular, we consider the relationship between Paschke duality and Spanier-Whitehead -duality.
Keywords
Cite
@article{arxiv.1609.00409,
title = {Spanier-Whitehead K-duality for $C^*$-algebras},
author = {Jerome Kaminker and Claude L. Schochet},
journal= {arXiv preprint arXiv:1609.00409},
year = {2017}
}
Comments
28 pages, Typos corrected and referees comments incorporated. To appear in Journal of Topology and Analysis