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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

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Simple inductive limit C*-algebras: Spectra and approximations by interval algebras

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 1999, Issue 507, Pages 57–79, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/crll.1999.507.57, June 2008

Publication History

Received:
1998-04-14
Accepted:
1998-07-27
Published Online:
2008-06-12

Abstract

Suppose that a simple C*-algebra A can be written as an inductive limit of , where Xn,i are finite CW complexes with uniformly bounded dimensions. Such inductive limit C*-algebras are called AH algebras.

In this paper, we will prove that for any n and ε > 0, there exists a homomorphism ψn,m: AnAm, which factors through an interval algebra , such that the spectra of ψn,m and the spectra of φn,m can be paired within ε provided that m is large enough. This result is essential for the classification of such simple C*-algebras.

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