Self-Similarity of Poisson structures on tori

• Autorzy: Kentaro Mikami , Alan Weinstein
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2000
• Tom: 51
• Numer: 1
• Strony: 211-217

Daty

wydano

2000

Twórcy

autor

Kentaro Mikami

• Department of Computer Science and Engineering, Faculty of Engineering and Resource Science, Akita University, Akita, 010-8502, Japan

autor

Alan Weinstein

• Department of Mathematics, University of California, Berkeley, CA 94720, U.S.A.

Bibliografia

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