Self-Similarity of Poisson structures on tori
Mikami, Kentaro ; Weinstein, Alan
Banach Center Publications, Tome 51 (2000), p. 211-217 / Harvested from The Polish Digital Mathematics Library

We study the group of diffeomorphisms of a 3-dimensional Poisson torus which preserve the Poisson structure up to a constant multiplier, and the group of similarity ratios.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:209033
@article{bwmeta1.element.bwnjournal-article-bcpv51z1p211bwm,
     author = {Mikami, Kentaro and Weinstein, Alan},
     title = {Self-Similarity of Poisson structures on tori},
     journal = {Banach Center Publications},
     volume = {51},
     year = {2000},
     pages = {211-217},
     zbl = {1010.53058},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv51z1p211bwm}
}
Mikami, Kentaro; Weinstein, Alan. Self-Similarity of Poisson structures on tori. Banach Center Publications, Tome 51 (2000) pp. 211-217. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv51z1p211bwm/

[000] [1] P. Iglésias, Arithmétique des rapports de similitudes symplectiques, Compositio Math. 95 (1995), 235-245.

[001] [2] P. Iglésias and G. Lachaud, Espaces différentiables singuliers et corps de nombres algébriques, Ann. Inst. Fourier (Grenoble) 40 (1990), 723-737. | Zbl 0703.57017

[002] [3] D. A. Marcus, Number Fields, Springer-Verlag, New York, 1977.

[003] [4] G. Prasad and M. S. Raghunathan, Cartan subgroups and lattices in semi-simple groups, Annals of Math. 96 (1972), 296-317. | Zbl 0245.22013

[004] [5] D. Shlyakhtenko, Von Neumann algebras and Poisson manifolds, survey article for Math 277, Spring 1997, Univ. of California, Berkeley, available at http://www.math.berkeley. edu/~alanw.

[005] [6] A. Weinstein, The modular automorphism group of a Poisson manifold, J. Geom. Phys. 23 (1997), 379-394. | Zbl 0902.58013

[006] [7] A. Weinstein, Poisson geometry, Diff. Geom. Appl. 9 (1998), 213-238.

[007] [8] A. Weinstein and P. Xu, Hochschild cohomology and characteristic classes for star-products, in: Topics in singularity theory: V.I. Arnold's 60th anniversary collection, A. Khovanskii, A. Varchenko, V. Vassiliev, eds., Amer. Math. Soc., Providence, 1997, 177-194.