Lie-Poisson structure on some Poisson Lie groups
Journal of the American Mathematical Society, Tome 05 (1992) no. 2, pp. 445-453

Voir la notice de l'article provenant de la source American Mathematical Society

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Ginzburg, Viktor L.; Weinstein, Alan. Lie-Poisson structure on some Poisson Lie groups. Journal of the American Mathematical Society, Tome 05 (1992) no. 2, pp. 445-453. doi: 10.1090/S0894-0347-1992-1126117-8

[1] Atiyah, M. F. Convexity and commuting Hamiltonians Bull. London Math. Soc. 1982 1 15

[2] Atiyah, M. F., Bott, R. The moment map and equivariant cohomology Topology 1984 1 28

[3] Bredon, Glen E. Introduction to compact transformation groups 1972

[4] Conn, Jack F. Normal forms for smooth Poisson structures Ann. of Math. (2) 1985 565 593

[5] Delzant, Thomas Hamiltoniens périodiques et images convexes de l’application moment Bull. Soc. Math. France 1988 315 339

[6] Drinfel′D, V. G. Hamiltonian structures on Lie groups, Lie bialgebras and the geometric meaning of classical Yang-Baxter equations Dokl. Akad. Nauk SSSR 1983 285 287

[7] Duistermaat, J. J. On the similarity between the Iwasawa projection and the diagonal part Mém. Soc. Math. France (N.S.) 1984 129 138

[8] Van Est, W. T. Une application d’une méthode de Cartan-Leray Nederl. Akad. Wetensch. Proc. Ser. A. 58 1955 542 544

[9] Fuks, D. B. Cohomology of infinite-dimensional Lie algebras 1986

[10] Guillemin, V., Sternberg, S. Convexity properties of the moment mapping Invent. Math. 1982 491 513

[11] Helgason, Sigurdur Differential geometry, Lie groups, and symmetric spaces 1978

[12] Kirwan, Frances Clare Cohomology of quotients in symplectic and algebraic geometry 1984

[13] Kostant, Bertram On convexity, the Weyl group and the Iwasawa decomposition Ann. Sci. École Norm. Sup. (4) 1973

[14] Koszul, Jean-Louis Crochet de Schouten-Nijenhuis et cohomologie Astérisque 1985 257 271

[15] Lu, Jiang-Hua, Ratiu, Tudor On the nonlinear convexity theorem of Kostant J. Amer. Math. Soc. 1991 349 363

[16] Lu, Jiang-Hua, Weinstein, Alan Poisson Lie groups, dressing transformations, and Bruhat decompositions J. Differential Geom. 1990 501 526

[17] Moser, Jã¼Rgen On the volume elements on a manifold Trans. Amer. Math. Soc. 1965 286 294

[18] Weinstein, Alan Some remarks on dressing transformations J. Fac. Sci. Univ. Tokyo Sect. IA Math. 1988 163 167

[19] Weinstein, Alan, Xu, Ping Extensions of symplectic groupoids and quantization J. Reine Angew. Math. 1991 159 189

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