The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Journal of Noncommutative Geometry


Full-Text PDF (265 KB) | Metadata | Table of Contents | JNCG summary
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