01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date:
17.01.1948
E-mail:
, ,
Keywords:
integrable systems,
Lie groups and Lie algebras,
representation theory,
quantumgroups,
symplectic geometry.
UDC:
512.4, 513.83
Subject:
Mathematical physics.
Main publications:
Harmonic analysis on Riemannian symmetric spaces of nonpositive
curvature and scattering theory. Sov. Math. Izv., 40, 1976, p. 562–592.
Current algebras and partial differential equations (with A. G. Reyman). Sov. Math. Doklady, 21, 1980, p. 630–634.
What is a classical r-matrix? Funct Anal. Appl. 17, 1983, p. 259–272.
Dressing transformations and Poisson group actions. Publ. RIMS, Kyoto University, 21, 1985, p. 1237–1260.
The Kowalewski top 99 years later: a Lax pair, generalizations, and
explicit solutions (with A. I. Bobenko, A. G. Reyman). Commun. Math. Phys., 122, 1989, p. 321–354.
Central extensions of quantum current algebras (with N. Reshetikhin). Lett. Math. Phys., 19, 1990, 133–139.
Group-Theoretical Methods in the Theory of Finite-Dimensional Integrable Systems (with A. Reyman). Encyclopaedia of Mathematical Sciences, vol. 16. Dynamical Systems VII. Ch. 2. Springer-Verlag, 1994, pp. 116–225.
Quantization of Open Toda Lattices. Encyclopaedia of Mathematical
Sciences, vol. 16. Dynamical Systems VII. Ch. 3. Springer-Verlag, 1994, pp. 226–259.
Poisson Lie groups, quantum duality principle, and the quantum double. Contemporary Mathematics, 178, 219–248, 1994.
Drinfeld-Sokolov reduction for difference operators and deformations of W-algebras. I. The case of Virasoro algebra (with E. Frenkel, N. Reshetikhin), Commun. Math. Phys, 192 (1998), 605–629.
Drinfeld-Sokolov reduction for difference operators and deformations of W-algebras. II. General semisimple case (with A. Sevostyanov). Commun. Math. Phys. 192 (1998), 631–646.
Unitary representations of $U_q(sl(2,\mathbf{R}))$, the modular double and the multiparticle q-deformed Toda chains. (with S. Kharchev, D. Lebedev). Commun. Math. Phys., 225, 573–609, 2002.
Integriruemye sistemy (teoretiko-gruppovoi podkhod). Moskva-Izhevsk 2003, 350 str. (sovm. s A. G. Reimanom).
L. A. Takhtajan, A. Yu. Alekseev, I. Ya. Aref'eva, M. A. Semenov-Tian-Shansky, E. K. Sklyanin, F. A. Smirnov, S. L. Shatashvili, “Scientific heritage of L. D. Faddeev. Survey of papers”, Uspekhi Mat. Nauk, 72:6(438) (2017), 3–112; Russian Math. Surveys, 72:6 (2017), 977–1081
M. A. Semenov-Tian-Shansky, “Lax operators, Poisson groups, and the differential Galois theory”, TMF, 181:1 (2014), 173–199; Theoret. and Math. Phys., 181:1 (2014), 1279–1301
M. A. Semenov-Tian-Shansky, “Poisson–Lie groups. The quantum duality principle and the twisted quantum double”, TMF, 93:2 (1992), 302–329; Theoret. and Math. Phys., 93:2 (1992), 1292–1307
M. A. Semenov-Tian-Shansky, “Monodromy mapping and classical $r$-matrices”, Zap. Nauchn. Sem. POMI, 200 (1992), 156–166; J. Math. Sci., 77:3 (1995), 3236–3242
A. G. Reiman, M. A. Semenov-Tian-Shansky, “Lax representation with a spectral parameter for the kowalevski top and its generalizations”, Funktsional. Anal. i Prilozhen., 22:2 (1988), 87–88; Funct. Anal. Appl., 22:2 (1988), 158–160
M. A. Olshanetsky, A. M. Perelomov, A. G. Reiman, M. A. Semenov-Tian-Shansky, “Integrable systems. II”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 16 (1987), 86–226
A. G. Reiman, M. A. Semenov-Tian-Shansky, “Compatible Poisson brackets for Lax equations and classical $r$-matrices”, Zap. Nauchn. Sem. LOMI, 164 (1987), 176–188
1986
8.
M. A. Semenov-Tian-Shansky, “Poisson groups and Dressing transformations”, Zap. Nauchn. Sem. LOMI, 150 (1986), 119–142
9.
A. G. Reiman, M. A. Semenov-Tian-Shansky, “Lie algebras and Lax equations with spectral parameter on an elliptic curve”, Zap. Nauchn. Sem. LOMI, 150 (1986), 104–118
A. G. Reiman, M. A. Semenov-Tian-Shansky, L. D. Faddeev, “Quantum anomalies and cocycles on gauge groups”, Funktsional. Anal. i Prilozhen., 18:4 (1984), 64–72; Funct. Anal. Appl., 18:4 (1984), 319–326
A. G. Reiman, M. A. Semenov-Tian-Shansky, “Hamiltonian structure of the Kadomzev–Petviashvily type equations”, Zap. Nauchn. Sem. LOMI, 133 (1984), 212–227
M. A. Semenov-Tian-Shansky, “What is a classical $r$-matrix?”, Funktsional. Anal. i Prilozhen., 17:4 (1983), 17–33; Funct. Anal. Appl., 17:4 (1983), 259–272
M. A. Semenov-Tian-Shansky, V. A. Franke, “Variational principle for the Lorentz gauge condition and nonperturbative bounds on the functional integration domain in nonabelian gauge theories”, Zap. Nauchn. Sem. LOMI, 120 (1982), 159–165
A. G. Reiman, M. A. Semenov-Tian-Shansky, “Current algebras and nonlinear partial differential equations”, Dokl. Akad. Nauk SSSR, 251:6 (1980), 1310–1314
A. G. Reiman, M. A. Semenov-Tian-Shansky, “A family of Hamiltonian structures, hierarchy of Hamiltonians, and reduction for first-order matrix differential operators”, Funktsional. Anal. i Prilozhen., 14:2 (1980), 77–78; Funct. Anal. Appl., 14:2 (1980), 146–148
A. G. Reiman, M. A. Semenov-Tian-Shansky, I. E. Frenkel, “Graded Lie algebras and completely integrable dynamical systems”, Dokl. Akad. Nauk SSSR, 247:4 (1979), 802–805
A. G. Izergin, V. E. Korepin, M. A. Semenov-Tian-Shansky, L. D. Faddeev, “Gauge conditions for the Yang–Mills field”, TMF, 38:1 (1979), 3–14; Theoret. and Math. Phys., 38:1 (1979), 1–9
M. A. Semenov-Tian-Shansky, “Harmonic analysis on Riemannian symmetric spaces of negative curvature and
scattering theory”, Izv. Akad. Nauk SSSR Ser. Mat., 40:3 (1976), 562–592; Math. USSR-Izv., 10:3 (1976), 535–563
M. A. Semenov-Tian-Shansky, “Harmonic analysis on symmetric Riemannian spaces of negative curvature and scattering theory”, Dokl. Akad. Nauk SSSR, 219:6 (1974), 1330–1333
I. Ya. Aref'eva, V. E. Zakharov, V. V. Kozlov, I. M. Krichever, V. P. Maslov, S. P. Novikov, A. M. Polyakov, N. Yu. Reshetikhin, M. A. Semenov-Tian-Shansky, E. K. Sklyanin, F. A. Smirnov, L. A. Takhtajan, S. L. Shatashvili, “Ludwig Dmitrievich Faddeev (obituary)”, Uspekhi Mat. Nauk, 72:6(438) (2017), 191–196; Russian Math. Surveys, 72:6 (2017), 1157–1163
2014
25.
I. Ya. Aref'eva, V. M. Buchstaber, E. P. Velikhov, A. B. Zhizhchenko, V. E. Zakharov, I. A. Ibragimov, S. V. Kislyakov, V. V. Kozlov, P. P. Kulish, L. N. Lipatov, V. P. Maslov, V. A. Matveev, S. P. Novikov, Yu. S. Osipov, A. M. Polyakov, V. A. Rubakov, M. A. Semenov-Tian-Shansky, Yu. A. Simonov, Ya. G. Sinai, A. A. Slavnov, I. A. Sokolov, L. A. Takhtadzhyan, V. E. Fortov, S. L. Shatashvili, “Ludvig Dmitrievich Faddeev (on his 80th birthday)”, Uspekhi Mat. Nauk, 69:6(420) (2014), 183–191; Russian Math. Surveys, 69:6 (2014), 1133–1142
Лаборатория математических проблем физики M. A. Semenov-Tian-Shansky Conference dedicated to the 90th anniversary of Steklov Mathematical Institute May 17, 2024 11:25