Cancellation and stable rank for direct limits of recursive subhomogeneous algebras

By N. Christopher Phillips. 2001

67 citations recorded by the source corpus.

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 --------------------------------------------------------------------------------

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d3ad258837c2b1131d2ac8ab5b8144a2364584c3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Minimal Dynamics and K-Theoretic Rigidity: Elliott’s Conjecture (2009, background): “1 (3) of [16] and [13, Proposition 16], respectively—a sketched proof of the latter result can be found in [14]).”
Crossed products by minimal homeomorphisms (2004, methodology): “The map K0ðAfygÞ ! K0ðAÞ is a group isomorphism by [35], Theorem 4.”
Large subalgebras (2014, methodology): “An early application of the one point version when X is not the Cantor set is in [22] and Section 4 of [29].”
Comparison Theory and Smooth Minimal C*-Dynamics (2008, background): “(In particular, A could by the C-algebra of a minimal diffeomorphism, as these have stable rank one by the main result of [23].”
Recursive subhomogeneous algebras (2001, background): “Algebras in this class, called recursive subhomogeneous algebras, can be expressed as iterated pullbacks of algebras of the form C(X,Mn), in such a way that an inductive argument reduces these theorems to “relative” versions of the same theorems for C(X,Mn).”