Cancellation and stable rank for direct limits of recursive subhomogeneous algebras

• Autores: N. Christopher Phillips
• Localización: Transactions of the American Mathematical Society, ISSN 0002-9947, Vol. 359, Nº 10, 2007, págs. 4625-4652
• Idioma: inglés
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• Resumen

  • We prove the following results for a unital simple direct limit of recursive subhomogeneous algebras with no dimension growth:

    (1) (2) The projections in satisfy cancellation: if then (3) satisfies Blackadar's Second Fundamental Comparability Question: if are projections such that for all normalized traces on then (4) is unperforated for the strict order: if and there is such that then The last three of these results hold under certain weaker dimension growth conditions and without assuming simplicity. We use these results to obtain previously unknown information on the ordered K-theory of the crossed product obtained from a minimal homeomorphism of a finite-dimensional infinite compact metric space Specifically, is unperforated for the strict order, and satisfies the following K-theoretic version of Blackadar's Second Fundamental Comparability Question: if satisfies for all normalized traces on then there is a projection such that --------------------------------------------------------------------------------