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# Journal of Noncommutative Geometry

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**Volume 11, Issue 4, 2017, pp. 1381–1393**

**DOI: 10.4171/JNCG/11-4-5**

Published online: 2017-12-15

Smooth crossed product of minimal unique ergodic diffeomorphism of odd sphere

Hongzhi Liu^{[1]}(1) Jilin University, Changchun, China

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 to $C(S^{2m+1})\rtimes_{\alpha_m} \mathbb{Z}$ even though $n\neq m$. However, by cyclic cohomology, we show that smooth crossed product algebra $C^\infty(S^{2n+1})\rtimes_{\alpha_n} \mathbb{Z}$ is not isomorphic to $C^\infty(S^{2m+1})\rtimes_{\alpha_m} \mathbb{Z}$ if~$n\neq m$.

*Keywords: *Smooth crossed products, cyclic cohomology

Liu Hongzhi: Smooth crossed product of minimal unique ergodic diffeomorphism of odd sphere. *J. Noncommut. Geom.* 11 (2017), 1381-1393. doi: 10.4171/JNCG/11-4-5