Classical r-matrices and the method of orbits
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Abstract
The geometric meaning of the classicalr-matrices of Yang-Baxter is discussed.
Keywords
Geometric Meaning
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Literature cited
- 1.E. K. Sklyanin, “Quantum version of the method of the inverse scattering problem,” J. Sov. Math.,19, No. 5 (1982).Google Scholar
- 2.L. D. Faddeev, “Quantum completely integrable models of field theory,” Preprint LOMI P-2-79, Leningrad (1979).Google Scholar
- 3.P. P. Kulish and E. K. Sklyanin, “Solutions of the Yang-Baxter equation,” J. Sov. Math.,19, No. 5 (1982).Google Scholar
- 4.A. A. Belavin and V. G. Drinfel'd, “Solutions of the classical Yang-Baxter equation for simple Lie algebras,” Funkts. Anal.,16, No. 3, 1–29 (1982).Google Scholar
- 5.M. Adler, “On a trace functional for formal pseudodifferential operators and the symplectic structure for Korteweg-de Vries type equations,” Inventiones Math.,50, 219–248 (1979).Google Scholar
- 6.B. Kostant, “Quantization and representation theory,” in: Proc. Research Symposium on Representations of Lie Groups, Oxford, 1977, London Math. Soc. Lecture Notes Series,34 (1979).Google Scholar
- 7.A. G. Reiman and M. A. Semenov-Tyan-Shanskii, “Algebras of flows and nonlinear partial differential equations,” Dokl. Akad. Nauk SSSR,251, No. 6 (1980).Google Scholar
- 8.A. G. Reyman and M. A. Semenov-Tian-Shansky, “Reduction of Hamiltonian systems, affine Lie algebras, and Lax equations, II,” Inventiones Math.,63, 423–432 (1981).Google Scholar
- 9.A. G. Reiman, “Integrable Hamiltonian systems associated with graded Lie algebras,” J. Sov. Math.,19, No. 5 (1982).Google Scholar
- 10.V. E. Zakharov and A. B. Shabat, “Integration of nonlinear equations of mathematical physics by the method of the inverse scattering problem. II,” Funkts. Anal.,13, No. 3, 13–22 (1979).Google Scholar
- 11.E. Date et al., “Transformation groups for soliton equations,” RIMS Preprint-394, Kyoto (1982).Google Scholar
- 12.A. V. Mikhailov, “The reduction problem and the inverse scattering method,” Physica D,3D, 73–117 (1981).Google Scholar
- 13.A. G. Reiman and M. A. Semenov-Tyan-Shanskii, “Family of Hamiltonian structures, hierarchy of Hamiltonians and reduction for first-order matrix differential operators,” Funkts. Anal.,11, No. 2, 77–78 (1980).Google Scholar
- 14.V. G. Drinfel'd and V. V. Sokolov, Dokl. Akad. Nauk SSSR,258, 11–14 (1981).Google Scholar
- 15.A. G. Reyman and M. A. Semenov-Tian-Shansky, “Reduction of Hamiltonian systems...I,” Inventiones Math.,54, 81–100 (1979).Google Scholar
- 16.S. Lie, Theorie der Transformationsgruppen, III,” Chap. 25, Sec. 115, Leipzig (1893).Google Scholar
- 17.L. D. Faddeev, Proc. l'Ecole d'Ete de Physique Theorique, Les Houches, North Holland (1982).Google Scholar
- 18.E. K. Sklyanin, “Algebraic structures associated with the Yang-Baxter equation,” Funkts. Analiz,16, No. 4, 27–34 (1982).Google Scholar
- 19.V. G. Drinfel'd, “Hamiltonian structures on Lie groups, Lie bialgebras and the geometric meaning of the classical Yang-Baxter equations,” Dokl. Akad. Nauk SSSR,267, No. 5, 1035–1041 (1982).Google Scholar
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© Plenum Publishing Corporation 1985