Self-Similarity of Poisson structures on tori

Kentaro Mikami; Alan Weinstein

Banach Center Publications (2000)

  • Volume: 51, Issue: 1, page 211-217
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Mikami, Kentaro, and Weinstein, Alan. "Self-Similarity of Poisson structures on tori." Banach Center Publications 51.1 (2000): 211-217. <http://eudml.org/doc/209033>.

@article{Mikami2000,
abstract = {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.},
author = {Mikami, Kentaro, Weinstein, Alan},
journal = {Banach Center Publications},
keywords = {Poisson structures; tori; self-similarities; scaling group},
language = {eng},
number = {1},
pages = {211-217},
title = {Self-Similarity of Poisson structures on tori},
url = {http://eudml.org/doc/209033},
volume = {51},
year = {2000},
}

TY - JOUR
AU - Mikami, Kentaro
AU - Weinstein, Alan
TI - Self-Similarity of Poisson structures on tori
JO - Banach Center Publications
PY - 2000
VL - 51
IS - 1
SP - 211
EP - 217
AB - 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.
LA - eng
KW - Poisson structures; tori; self-similarities; scaling group
UR - http://eudml.org/doc/209033
ER -

References

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  1. [1] P. Iglésias, Arithmétique des rapports de similitudes symplectiques, Compositio Math. 95 (1995), 235-245. 
  2. [2] P. Iglésias and G. Lachaud, Espaces différentiables singuliers et corps de nombres algébriques, Ann. Inst. Fourier (Grenoble) 40 (1990), 723-737. Zbl0703.57017
  3. [3] D. A. Marcus, Number Fields, Springer-Verlag, New York, 1977. 
  4. [4] G. Prasad and M. S. Raghunathan, Cartan subgroups and lattices in semi-simple groups, Annals of Math. 96 (1972), 296-317. Zbl0245.22013
  5. [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. 
  6. [6] A. Weinstein, The modular automorphism group of a Poisson manifold, J. Geom. Phys. 23 (1997), 379-394. Zbl0902.58013
  7. [7] A. Weinstein, Poisson geometry, Diff. Geom. Appl. 9 (1998), 213-238. 
  8. [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. 

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