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Decomposition Rank of Subhomogeneous C*‐Algebras
Author(s) -
Winter Wilhelm
Publication year - 2004
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611504014716
Subject(s) - mathematics , rank (graph theory) , decomposition , pure mathematics , combinatorics , chemistry , organic chemistry
We analyze the decomposition rank (a notion of covering dimension for nuclear C*‐algebras introduced by E. Kirchberg and the author) of subhomogeneous C*‐algebras. In particular, we show that a subhomogeneous C*‐algebra has decomposition rank n if and only if it is recursive subhomogeneous of topological dimension n , and that n is determined by the primitive ideal space. As an application, we use recent results of Q. Lin and N. C. Phillips to show the following. Let A be the crossed product C*‐algebra coming from a compact smooth manifold and a minimal diffeomorphism. Then the decomposition rank of A is dominated by the covering dimension of the underlying manifold. 2000 Mathematics Subject Classification 46L85, 46L35.