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Funktsional. Anal. i Prilozhen., 1981, Volume 15, Issue 3, Pages 23–40 (Mi faa1729)  

This article is cited in 20 scientific papers (total in 22 papers)

Hamiltonian operators and infinite-dimensional Lie algebras

I. M. Gel'fand, I. Ya. Dorfman


Full text: PDF file (1906 kB)
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English version:
Functional Analysis and Its Applications, 1981, 15:3, 173–187

Bibliographic databases:

UDC: 519.46
Received: 25.03.1981

Citation: I. M. Gel'fand, I. Ya. Dorfman, “Hamiltonian operators and infinite-dimensional Lie algebras”, Funktsional. Anal. i Prilozhen., 15:3 (1981), 23–40; Funct. Anal. Appl., 15:3 (1981), 173–187

Citation in format AMSBIB
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\by I.~M.~Gel'fand, I.~Ya.~Dorfman
\paper Hamiltonian operators and infinite-dimensional Lie algebras
\jour Funktsional. Anal. i Prilozhen.
\yr 1981
\vol 15
\issue 3
\pages 23--40
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=630337}
\zmath{https://zbmath.org/?q=an:0478.58013}
\transl
\jour Funct. Anal. Appl.
\yr 1981
\vol 15
\issue 3
\pages 173--187
\crossref{https://doi.org/10.1007/BF01089922}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. P. Novikov, “The Hamiltonian formalism and a many-valued analogue of Morse theory”, Russian Math. Surveys, 37:5 (1982), 1–56  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. I. M. Gel'fand, I. Ya. Dorfman, “Hamiltonian operators and the classical Yang–Baxter equation”, Funct. Anal. Appl., 16:4 (1982), 241–248  mathnet  crossref  mathscinet  zmath  isi
    3. I. M. Gel'fand, I. V. Cherednik, “The abstract Hamiltonian formalism for the classical Yang–Baxter bundles”, Russian Math. Surveys, 38:3 (1983), 1–22  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. N. N. Bogolyubov, S. G. Gindikin, A. A. Kirillov, A. N. Kolmogorov, S. P. Novikov, L. D. Faddeev, “Izrail' Moiseevich Gel'fand (on his seventieth birthday)”, Russian Math. Surveys, 38:6 (1983), 145–153  mathnet  crossref  mathscinet  zmath  adsnasa
    5. S. P. Novikov, “The geometry of conservative systems of hydrodynamic type. The method of averaging for field-theoretical systems”, Russian Math. Surveys, 40:4 (1985), 85–98  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. A. O. Radul, “A description of Poisson brackets on a space of nonlocal functionals”, Funct. Anal. Appl., 19:2 (1985), 153–156  mathnet  crossref  mathscinet  zmath  isi
    7. Yu. L. Daletskii, “Hamiltonian operators in graded formal calculus of variations”, Funct. Anal. Appl., 20:2 (1986), 136–138  mathnet  crossref  mathscinet  zmath  isi
    8. T. G. Khovanova, “The Gel'fand–Dikii Lie Algebras and the Virasoro algebra”, Funct. Anal. Appl., 20:4 (1986), 332–334  mathnet  crossref  mathscinet  zmath  isi
    9. T. G. Khovanova, “Korteweg–de Vries superequation related to the Lie superalgebra of Neveu-Schwarz-2 string theory”, Theoret. and Math. Phys., 72:2 (1987), 899–904  mathnet  crossref  mathscinet  zmath  isi
    10. V. A. Arkad'ev, A. K. Pogrebkov, M. K. Polivanov, “Expansions with respect to squares, symplectic and poisson structures associated with the Sturm–Liouville problem. I”, Theoret. and Math. Phys., 72:3 (1987), 909–920  mathnet  crossref  mathscinet  zmath  isi
    11. V. Yu. Ovsienko, B. A. Khesin, “Korteweg–de Vries superequation as an Euler equation”, Funct. Anal. Appl., 21:4 (1987), 329–331  mathnet  crossref  mathscinet  zmath  isi
    12. O. I. Mokhov, “Dubrovin–Novikov type Poisson brackets (DN-brackets)”, Funct. Anal. Appl., 22:4 (1998), 336–338  mathnet  crossref  mathscinet  zmath
    13. B. A. Dubrovin, S. P. Novikov, “Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory”, Russian Math. Surveys, 44:6 (1989), 35–124  mathnet  crossref  mathscinet  zmath  adsnasa
    14. O. I. Mokhov, “Canonical variables for the two-dimensional hydrodynamics of an incompressible fluid with vorticity”, Theoret. and Math. Phys., 78:1 (1989), 97–99  mathnet  crossref  mathscinet  zmath  isi
    15. O. I. Mokhov, “A Hamiltonian structure of evolution in the space variable $x$ for the Korteweg–de Vries equation”, Russian Math. Surveys, 45:1 (1990), 218–220  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    16. M. N. Araslanov, Yu. L. Daletskii, “Composite logarithm in the class of formal operator power series”, Funct. Anal. Appl., 26:2 (1992), 121–124  mathnet  crossref  mathscinet  zmath  isi
    17. O. I. Mokhov, S. P. Novikov, A. K. Pogrebkov, “Irina Yakovlevna Dorfman (obituary)”, Russian Math. Surveys, 50:6 (1995), 1241–1246  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    18. O. I. Mokhov, “Symplectic and Poisson structures on loop spaces of smooth manifolds, and integrable systems”, Russian Math. Surveys, 53:3 (1998), 515–622  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    19. O. I. Mokhov, “Quasi-Frobenius Algebras and Their Integrable $N$-Parameter Deformations Generated by Compatible $(N\times N)$ Metrics of Constant Riemannian Curvature”, Theoret. and Math. Phys., 136:1 (2003), 908–916  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    20. P. Ya. Grozman, D. A. Leites, “Nonholonomic Riemann and Weyl tensors for flag manifolds”, Theoret. and Math. Phys., 153:2 (2007), 1511–1538  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    21. O. I. Mokhov, “The Classification of Nonsingular Multidimensional Dubrovin–Novikov Brackets”, Funct. Anal. Appl., 42:1 (2008), 33–44  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    22. Wang Ya. Hou D. Bai Ch., “Operator Forms of the Classical Yang–Baxter Equation in Lie Superalgebras”, Int. J. Geom. Methods Mod. Phys., 7:4 (2010), 583–597  crossref  isi
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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