• Corpus ID: 119282764

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

@article{Liu2016TwoMU,
  title={Two minimal unique ergodic diffeomorphisms on a manifolds and their smooth crossed product algebras},
  author={Hongzhi Liu},
  journal={arXiv: Operator Algebras},
  year={2016}
}
  • Hongzhi Liu
  • Published 1 May 2016
  • Mathematics
  • arXiv: Operator Algebras
In this article we construct two minimal unique ergodic diffeomorphisms $\alpha$ and $\beta$ on $S^3 \times S^{6} \times S^{8} $. We will show that $C(S^3 \times S^{6} \times S^{8}) \rtimes_\alpha \mathbb{Z} $ and $C(S^3 \times S^{6} \times S^{8})\rtimes_\beta \mathbb{Z} $ are equivalent to each other, while $C^\infty (S^3 \times S^{6} \times S^{8})\rtimes_\alpha \mathbb{Z} $ and $C^\infty(S^3 \times S^{6} \times S^{8} )\rtimes_\beta \mathbb{Z} $ are not. 

References

SHOWING 1-10 OF 18 REFERENCES
Smooth crossed products induced by minimal unique ergodic diffeomorphisms on odd spheres
For minimal unique ergodic diffeomorphisms $\alpha_n$ of $S^{2n+1} (n>0)$ and $\alpha_m$ of $S^{2m+1}(m>0)$, the $C^*$-crossed product algebra $C(S^{2n+1})\rtimes_{\alpha_n} \mathbb{Z}$ is isomorphic
Minimal Dynamics and K-Theoretic Rigidity: Elliott’s Conjecture
Let X be a compact infinite metric space of finite covering dimension and α : X → X a minimal homeomorphism. We prove that the crossed product $${\mathcal{C}(X) \rtimes_\alpha \mathbb{Z}}$$ absorbs
MINIMAL BUT NOT UNIQUELY ERGODIC DIFFEOMORPHISMS
If f is a uniquely ergodic transformation on a separable metric space preserving a Borel measure μ then f |supp(μ) is minimal, that is every orbit is dense [7, Proposition 4.1.18]. It was therefore a
Dense m-convex Frechet Subalgebras of Operator Algebra Crossed Products by Lie Groups
Let A be a dense Frechet *-subalgebra of a C*-algebra B. (We do not require Frechet algebras to be m-convex.) Let G be a Lie group, not necessarily connected, which acts on both A and B by
An analogue of the thom isomorphism for crossed products of a C∗ algebra by an action of R
Abstract In this paper we show the existence and uniqueness of a natural isomorphism ojα of Kj(A) with Kj+1(A ⋊α R ), j ϵ Z /2 where (A, R , α) is a C∗ dynamical R -system, K is the functor of
Topological orbit equivalence and C*-crossed products.
The present paper has one foot within the theory of topological dynamical Systems and the other within C*-algebra theory. The link between the two is provided by Ktheory via the crossed product
C∗-algebras associated with irrational rotations
For any irrational number a let Aa be the transformation group C*-algebra for the action of the integers on the circle by powers of the rotation by angle 2πa. It is known that Aa is simple and has a
Strict Ergodicity and Transformation of the Torus
Introduction. If T is a measure preserving transformation ofl a probability space Q with measure Iu, the ergodic theorem assures the existence N-1 almost everywhere with respect to /i of the average
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
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
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