What is a classical r-matrix?
Tóm tắt
Từ khóa
Tài liệu tham khảo
E. K. Sklyanin, "On complete integrability of the Landau?Lifshitz equation," Preprint LOMI, E-3-79, Leningrad, LOMI (1980).
E. K. Sklyanin, "The quantum inverse scattering method," Zap. Nauchn. Sem. LOMI,95, 55?128 (1980).
A. A. Belavin and V. G. Drinfel'd, "On the solutions to the classical Yang?Baxter equation for simple Lie algebras," Funkts. Anal. 16, No. 3, 1?29 (1982).
4.A. A. Belavin and V. G. Drinfel'd, "Triangle equations and simple Lie algebras," Preprint ITF 1982-18, Chernogolovka, ITF.
V. G. Drinfel'd, "Hamiltonian structures on Lie groups, Lie bialgebras, and the geometrical meaning of the Yang?Baxter equations," Dokl. Akad. Nauk SSSR,268, No. 2, 285?287 (1983).
L. D. Faddeev, "Integrable models in 1 + 1 dimensional quantum field theory," Preprint S.Ph.T. 82/76, CEN Saclay (1982).
M. A. Semenov-Tyan-Shanskii, "Classical r-matrices and the orbit method," Zap. Nauchn. Sem. LOMI,123, 77?91 (1983).
A. G. Reyman, and M. A. Semenov-Tyan-Shanskii, "Algebras of currents and nonlinear partial differential equations," Dokl. Akad. Nauk SSSR,251, No. 6, 1310?1313 (1980).
A. G. Reyman, "Integrable Hamiltonian systems connected with graded Lie algebras," Zap. Nauchn. Sem. LOMI,95, 3?54 (1980).
M. Adler and P. van Moerbeke, "Completely integrable systems, Euclidean Lie algebras, and curves," Adv. Math.,38, No. 2, 267?317 (1980).
A. G. Reyman and M. A. Semenov-Tyan-Shanskii [Semenov-Trian-Shansky], "Reduction of Hamiltonian systems, affine Lie algebras, and Lax equations, I, II," Invent. Math.,54, No. 1, 81?100 (1979), and63, No. 3, 423?432 (1981).
P. P. Kulish and A. G. Reyman, "Hamiltonian structure of polynomial bundles," Zap. Nauchn. Sem. LOMI,123, 67?76 (1983).
S. Lie (Unter Mitwirkung von F. Engel), Theorie der Transformationsgruppen, Bd. 1?3, Teubner, Leiptzig (1888, 1890, 1893).
B. Kostant, "Quantization and representation theory," in: Proc. Research Symp. on Representations of Lie groups, Oxford 1977, London Math. Soc. Lecture Notes Series, Vol. 34 (1979).
M. Adler, "On a trace functional for formal pseudodifferential operators and the symplectic structure for the KdV type equations," Invent. Math.,50, No. 2, 219?248 (1979).
N. I. Muskhelishvili, Singular Integral Equations [in Russian], Nauka, Moscow (1968).
E. K. Sklyanin, "Some algebraic structures connected with the Yang?Baxter equation," Funkts. Anal.,16, No. 4, 27?34 (1982).
I. M. Gel'fand and I. Ya. Dorfman, "Hamiltonian operators and the classical Yang?Baxter equation," Funkts. Anal., 16, No. 4, 1?9 (1982). 1?9 (1982).
I. M. Gel'fand and I. Ya. Dorfman, "Schouten brackets and Hamiltonian operators," Funkts. Anal.,14, No. 3, 71?74 (1980).
I. M. Gel'fand and L. A. Dikii, "A family of Hamiltonian structures connected with nonlinear integrable equations," Preprint IPM Akad. Nauk SSSR, No. 136, IPM, Moscow (1978).
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).
I. M. Glazman and Yu. I. Lyubich, Finite-Dimensional Linear Analysis in Problems [in Russian], Nauka, Moscow (1969).