Semenov-Tian-Shansky, Michael Arsen'evich

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Total publications: 25
Scientific articles: 23
Presentations: 1

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Doctor of physico-mathematical sciences (1985)
Speciality: 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


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).
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List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. 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  mathnet  mathscinet  elib; Russian Math. Surveys, 72:6 (2017), 977–1081  isi  scopus
2. M. A. Semenov-Tian-Shansky, “Lax operators, Poisson groups, and the differential Galois theory”, TMF, 181:1 (2014),  173–199  mathnet  mathscinet  elib; Theoret. and Math. Phys., 181:1 (2014), 1279–1301  isi  elib  scopus
3. M. A. Semenov-Tian-Shansky, “Poisson–Lie groups. The quantum duality principle and the twisted quantum double”, TMF, 93:2 (1992),  302–329  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 93:2 (1992), 1292–1307  isi
4. M. A. Semenov-Tian-Shansky, “Monodromy mapping and classical $r$-matrices”, Zap. Nauchn. Sem. POMI, 200 (1992),  156–166  mathnet  mathscinet  zmath; J. Math. Sci., 77:3 (1995), 3236–3242
5. 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  mathnet  mathscinet; Funct. Anal. Appl., 22:2 (1988), 158–160  isi
6. 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  mathnet  mathscinet  zmath
7. 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  mathnet  zmath
8. M. A. Semenov-Tian-Shansky, “Poisson groups and Dressing transformations”, Zap. Nauchn. Sem. LOMI, 150 (1986),  119–142  mathnet  zmath
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  mathnet  zmath
10. 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  mathnet  mathscinet  zmath; Funct. Anal. Appl., 18:4 (1984), 319–326  isi
11. M. A. Semenov-Tian-Shansky, “Classical $r$-matrices and quantization”, Zap. Nauchn. Sem. LOMI, 133 (1984),  228–235  mathnet  mathscinet  zmath
12. A. G. Reiman, M. A. Semenov-Tian-Shansky, “Hamiltonian structure of the Kadomzev–Petviashvily type equations”, Zap. Nauchn. Sem. LOMI, 133 (1984),  212–227  mathnet  mathscinet  zmath
13. M. A. Semenov-Tian-Shansky, “What is a classical $r$-matrix?”, Funktsional. Anal. i Prilozhen., 17:4 (1983),  17–33  mathnet  mathscinet  zmath; Funct. Anal. Appl., 17:4 (1983), 259–272  isi
14. D. A. Leites, M. A. Semenov-Tian-Shansky, “Integrable systems and Lie superalgebras”, Zap. Nauchn. Sem. LOMI, 123 (1983),  92–97  mathnet  mathscinet  zmath
15. M. A. Semenov-Tian-Shansky, “Classical $r$-matrices and the orbits method”, Zap. Nauchn. Sem. LOMI, 123 (1983),  77–91  mathnet  mathscinet  zmath
16. 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  mathnet  mathscinet  zmath
17. A. G. Reiman, M. A. Semenov-Tian-Shansky, “Current algebras and nonlinear partial differential equations”, Dokl. Akad. Nauk SSSR, 251:6 (1980),  1310–1314  mathnet  mathscinet  zmath
18. 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  mathnet  mathscinet  zmath; Funct. Anal. Appl., 14:2 (1980), 146–148
19. 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  mathnet  mathscinet  zmath
20. 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  mathnet  mathscinet; Theoret. and Math. Phys., 38:1 (1979), 1–9
21. 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  mathnet  mathscinet  zmath; Math. USSR-Izv., 10:3 (1976), 535–563
22. 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  mathnet  mathscinet  zmath
23. M. A. Semenov-Tian-Shansky, “A certain property of the Kirillov integral”, Zap. Nauchn. Sem. LOMI, 37 (1973),  53–65  mathnet  mathscinet  zmath

24. 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  mathnet  mathscinet  elib; Russian Math. Surveys, 72:6 (2017), 1157–1163  isi
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  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 69:6 (2014), 1133–1142  isi

Presentations in Math-Net.Ru
1. Scattering on the Poincaré upper half-plane, Riemann hypothesis, intertwining operators and Huygens principle
M. A. Semenov-Tian-Shansky
General Mathematics Seminar of the St. Petersburg Division of Steklov Institute of Mathematics, Russian Academy of Sciences
February 26, 2018 13:00   

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