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Localizing subcategories in the Bootstrap category of separable C*-algebras

Published online by Cambridge University Press:  15 September 2010

Ivo Dell'Ambrogio
Ivo Dell'Ambrogio
Affiliation:
Dpt. of Mathematics, Faculty of Science, National University of Singapore (NUS), 10 Lower Kent Ridge Road, S17-08-22, Singapore, 117543. ivo@dellambrogio.ch
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Abstract

Using the classical universal coefficient theorem of Rosenberg-Schochet, we prove a simple classification of all localizing subcategories of the Bootstrap category Boot ⊂ KK of separable complex C*-algebras. Namely, they are in a bijective correspondence with subsets of the Zariski spectrum Specℤ of the integers – precisely as for the localizing subcategories of the derived category D(ℤ) of complexes of abelian groups. We provide corollaries of this fact and put it in context with the similar classifications available in the literature.

Keywords

KK-theorylocalizing subcategoriesuniversal coefficient theorem
Type
Research Article
Information
Journal of K-Theory , Volume 8 , Issue 3 , December 2011 , pp. 493 - 505
Copyright
Copyright © ISOPP 2010

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