Two results on a class of Poisson structures on Lie groups

• [A] Adler, M.: On a trace functional for formal pseudo-differential operators and the symplectic strucure of the Korteweg-de Vries type equations. Invent. Math.50, 219–248 (1979)

  Article  MATH  Google Scholar 

• [AvM] Adler, M., van Moerbeke, P.: Completely integrable systems, Euclidean Lie algebras, and curves. Adv. Math.36, 267–317 (1980)

  Article  Google Scholar 

• [DL] Deift, P., Li, L.C.: Poisson geometry of the analog of the Miura maps and Bäcklund-Darboux transformations for equations of Toda type and periodic Toda flows. Commun. Math. Phys. 143, 201–214 (1991)

  Article  MATH  MathSciNet  Google Scholar 

• [Dr] Drinfeld, V.: Hamiltonian structures on Lie groups, Lie bialgebras and the geometric meaning of the classical Yang-Baxter equations. Sov. Math., Dokl.27, 68–71 (1983)

  MathSciNet  Google Scholar 

• [FT] Faddeev, L.D., Takhtadzhyan, L.A.: Hamiltonian, methods in the theory of solitons. Berlin Heidelberg New York: Springer 1987

  MATH  Google Scholar 

• [H] Helgason, S.: Differential geometry, Lie groups, and symmetric spaces. New York: Academic Press 1978

  MATH  Google Scholar 

• [K] Kostant, B.: Quantization and represetation theory. In: Proc. Research Symposium on Representations of Lie Groups. Oxford 1977. (Lond. Math. Soc. Lect. Notes Ser., vol. 34) Cambridge: Cambridge University Press 1979

  Google Scholar 

• [L] Li, L.C.: The SVD flow on generic symplectic leaves are completely integrable (preprint)

• [LP1] Li, L. C., Parmentier, S.: A new class of quadratic Poisson structures and the Yang-Baxter equation. C.R. Acad. Sci., Paris Sér. I307, 279–281 (1988); Nonlinear Poisson structures andr-matrices. Commun. Math. Phys.125, 545–563 (1989)

  MATH  MathSciNet  Google Scholar 

• [LP2] Li, L.C., Parmentier, S.: Modified structures associated with Poisson Lie groups. In: Ratiu, T. (ed.): The Geometry of Hamiltonian Systems (Publ., Math. Sci. Res. Inst., vol. 22). Berlin Heidelberg New York: Springer 1991

  Google Scholar 

• [LW] Lu, J.H., Weinstein, A.: Poisson Lie groups, dressing transformation and Bruhat decompositions. J. Differ. Geom.31, 502–526 (1990)

  MathSciNet  Google Scholar 

• [STS1] Semenov-Tian-Shansky, M.A.: What is a classicalr-matrix? Funct. Anal. Appl.17, 259–272 (1983)

  Article  Google Scholar 

• [STS2] Semenov-Tian-Shansky, M.A.: Dressing transformations and Poisson Lie group actions. Publ. Res. Inst. Math. Sci.21, 1237–1260 (1985)

  MathSciNet  Google Scholar 

• [S] Symes, W. W.: Systems of Toda type, inverse spectral problems and representation theory. Invent. Math.59, 13–51 (1980)

  Article  MATH  MathSciNet  Google Scholar 

• [V] Varadarajan, V.S.: Lie groups, Lie algebras, and their representations. Berlin Heidelberg New York: Springer 1984

  MATH  Google Scholar 

Download references