Comparison Theory and Smooth Minimal C*-Dynamics
By Andrew S. Toms. 2008
48 citations recorded by the source corpus.
We prove that the C*-algebra of a minimal diffeomorphism satisfies Blackadar’s Fundamental Comparability Property for positive elements. This leads to the classification, in terms of K-theory and traces, of the isomorphism classes of countably generated Hilbert modules over such algebras, and to a similar classification for the closures of unitary orbits of self-adjoint elements. We also obtain a structure theorem for the Cuntz semigroup in this setting, and prove a conjecture of Blackadar and Handelman: the lower semicontinuous dimension functions are weakly dense in the space of all dimension functions. These results continue to hold in the broader setting of unital simple ASH algebras with slow dimension growth and stable rank one. Our main tool is a sharp bound on the radius of comparison of a recursive subhomogeneous C*-algebra. This is also used to construct uncountably many non-Morita-equivalent simple separable amenable C*-algebras with the same K-theory and tracial state space, providing a C*-algebraic analogue of McDuff’s uncountable family of II1 factors. We prove in passing that the range of the radius of comparison is exhausted by simple C*-algebras.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/2bce8b6cf385ca71c8ba86099fbc2c2eeb7cd737
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In Applied Mathematics
- Leonel Robert
- W. Winter
- Aaron Tikuisis
- Andrew S. Toms
- B. Blackadar
- G'abor Szab'o
- M. Rørdam
- Ilan Hirshberg
In Mathematical Physics
- W. Winter
- Aaron Tikuisis
- Leonel Robert
- Andrew S. Toms
- G'abor Szab'o
- B. Blackadar
- F. Perera
- David Kerr
Citations in the corpus
- An algebraic approach to the radius of comparison (2010, methodology): “It has since proved useful in distinguishing simple C∗-algebras having the same K-theory and traces (see [20] and [8]); [8] is particularly interesting, as it suggests a connection between the radius of comparison of a crossed product C∗-algebra and the mean dimension of the underlying topological d”