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COVERING DIMENSION AND QUASIDIAGONALITY

EBERHARD KIRCHBERG

Humboldt–Universität zu Berlin, Institut für Mathematik, Unter den Linden 6, D-10099 Berlin, Germany

Current address: Mathematisches Institut der Universität Münster, Einsteinstr. 62, D-48149 Münster, Germany

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and

WILHELM WINTER

Mathematisches Institut der Universität Münster, Einsteinstr. 62, D-48149 Münster, Germany

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https://doi.org/10.1142/S0129167X04002119Cited by:80 (Source: Crossref)

Abstract

We introduce the decomposition rank, a notion of covering dimension for nuclear C*-algebras. The decomposition rank generalizes ordinary covering dimension and has nice permanence properties; in particular, it behaves well with respect to direct sums, quotients, inductive limits, unitization and quasidiagonal extensions. Moreover, it passes to hereditary subalgebras and is invariant under stabilization. It turns out that the decomposition rank can be finite only for strongly quasidiagonal C*-algebras and that it is closely related to the classification program.

Keywords:

AMSC: 46L85, 46L35

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