- journal article metadata
European Mathematical Society Publishing House
2017-12-18 23:40:02
Journal of Noncommutative Geometry
J. Noncommut. Geom.
JNCG
1661-6952
1661-6960
Global analysis, analysis on manifolds
General
10.4171/JNCG
http://www.ems-ph.org/doi/10.4171/JNCG
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
11
2017
4
Smooth crossed product of minimal unique ergodic diffeomorphism of odd sphere
Hongzhi
Liu
Jilin University, Changchun, China
Smooth crossed products, cyclic cohomology
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~$n\neq m$.
$K$-theory
Functional analysis
Global analysis, analysis on manifolds
1381
1393
10.4171/JNCG/11-4-5
http://www.ems-ph.org/doi/10.4171/JNCG/11-4-5
12
15
2017