Direct limit decomposition for C*-algebras of minimal diffeomorphisms

Qing Lin, N. Christopher Phillips

备注：: 20 pages, AMSLaTeX. To appear in the proceedings of the US-Japan Operator Algebra Conference in Fukuoka (1999). Some conjectures in this survey have since been proved

英文摘要：

This is a survey article describing the proof that the crossed product C^* (Z, M, h) of a compact smooth manifold M by a minimal diffeomorphism h of M is isomorphic to a direct limit of recursive subhomogeneous C*-algebras.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

When are crossed products by minimal diffeomorphisms isomorphic?

This is a survey which discusses the isomorphism problem for both C* and smooth crossed products by minimal diffeomorphisms. For C* crossed products, examples demonstrate the failure of the obvious analog of the Giordano-Putnam-Skau Theorem on minimal homeomorphisms of the Cantor set. For smooth crossed products, there are many open problems.

2002-08-11math.OA

Two minimal unique ergodic diffeomorphisms on a manifolds and their smooth crossed product algebras

In this article we construct two minimal unique ergodic diffeomorphisms $α$ and $β$ on $S^3 \times S^{6} \times S^{8} $. We will show that $C(S^3 \times S^{6} \times S^{8}) \rtimes_α\mathbb{Z} $ and $C(S^3 \times S^{6} \times S^{8})\rtimes_β\mathbb{Z} $ are equivalent to each other, while $C^\infty (S^3 \times S^{6} \times S^{8})\rtimes_α\mathbb{Z} $ and $C^\infty(S^3 \times S^{6} \times S^{8} )\rtimes_β\mathbb{Z} $ are not.

2016-05-20math.OA

Smooth crossed products induced by minimal unique ergodic diffeomorphisms on odd spheres

For minimal unique ergodic diffeomorphisms $α_n$ of $S^{2n+1} (n>0)$ and $α_m$ of $S^{2m+1}(m>0)$, the $C^*$-crossed product algebra $C(S^{2n+1})\rtimes_{α_n} \mathbb{Z}$ is isomorphic to $C(S^{2m+1})\rtimes_{α_m} \mathbb{Z}$ even though $n\neq m$ . However, by cyclic cohomology, we show that smooth crossed product algebra $C^\infty(S^{2n+1})\rtimes_{α_n} \mathbb{Z}$ is not isomorphic to $C^\infty(S^{2m+1})\rtimes_{α_m} \mathbb{Z}$ if $n\neq m$.

2016-04-06math.OA

Examples of different minimal diffeomorphisms giving the same C*-algebras

We give examples of minimal diffeomorphisms of compact connected manifolds which are not topologically orbit equivalent, but whose transformation group C*-algebras are isomorphic. The examples show that the following properties of a minimal diffeomorphism are not invariants of the transformation group C*-algebra: having topologically quasidiscrete spectrum; the action on singular cohomology (when the manifolds are diffeomorphic); the homotopy type of the manifold (when the manifolds have the same dimension); and the dimension of the manifold. These examples also give examples of nonconjugate i…

2004-08-22math.DSmath.OA

Decomposition rank of subhomogeneous $C^*$-algebras

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 th…

2002-10-28math.FAmath.OA

C*-algebras of minimal dynamical systems of the product of a Cantor set and an odd dimensional sphere

Let β: S^n \to S^n, for n = 2k + 1, k \geq 1, be one of the known examples of a non-uniquely ergodic minimal diffeomorphism of an odd dimensional sphere. For every such minimal dynamical system (S^n, β) there is a Cantor minimal system (X, α) such that the corresponding product system (X x S^n, αx β) is minimal and the resulting crossed product C*-algebra C(X x S^n) \rtimes_{αx β} \mathbb{Z} is tracially approximately an interval algebra (TAI). This entails classification for such C*-algebras. Moreover, the minimal Cantor system (X, α) is such that each tracial state on C(X x S^n) \rtimes_β \m…

2014-10-17math.DSmath.OA