Crossed products by minimal homeomorphisms
By Huaxin Lin, N. Christopher Phillips. 2004
75 citations recorded by the source corpus.
Abstract Let X be an infinite compact metric space with finite covering dimension and let h : X → X be a minimal homeomorphism. We show that the associated crossed product C*-algebra A = C*(ℤ, X, h) has tracial rank zero whenever the image of K 0(A) in Aff(T(A)) is dense. As a consequence, we show that these crossed product C*-algebras are in fact simple AH algebras with real rank zero. When X is connected and h is further assumed to be uniquely ergodic, then the above happens if and only if the rotation number associated to h has irrational values. By applying the classification result for nuclear simple C*-algebras with tracial rank zero, we show that two such dynamical systems have isomorphic crossed products if and only if they have isomorphic scaled ordered K-theory.
Subfields: Algebra and Number Theory, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/e7433d9bba4134e52498bd48ba5cb5d2a2e0e3b0
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In Algebra and Number Theory
- W. Winter
- Andrew S. Toms
- G'abor Szab'o
- Z. Niu
- G. Elliott
- David Kerr
- N. Christopher Phillips
- Huaxin Lin
In Mathematical Physics
- W. Winter
- Andrew S. Toms
- G'abor Szab'o
- David Kerr
- Z. Niu
- G. Elliott
- N. Christopher Phillips
- Huaxin Lin
Citations in the corpus
- Almost Finiteness and the Small Boundary Property (2018, background): “valence instead of a probability measure. While towers and tower decompositions have long played an important role in unraveling the structure of C∗-crossed products, notably in the case of Z-actions [35, 26, 25, 39, 13] and in the various theories of dimension for group actions [18, 36, 37, 21], th”
- Large subalgebras (2014, background): “• The one point version plays a key role in [20].”
- On tracial approximation (2008, background): “In this way, the higher-dimensional simple noncommutative tori were shown to be AT-algebras in [22] and [29], and the crossed-product C*-algebras arising from certain minimal homeomorphisms were shown to be AH-algebras in [24].”
- Minimal Dynamics and K-Theoretic Rigidity: Elliott’s Conjecture (2009, background): “6 Next, we recall another result from [10].”