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Funktsional. Anal. i Prilozhen., 1987, Volume 21, Issue 2, Pages 46–63 (Mi faa1190)  

This article is cited in 64 scientific papers (total in 65 papers)

Algebras of virasoro type, riemann surfaces and structures of the theory of solitons

I. M. Krichever, S. P. Novikov

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English version:
Functional Analysis and Its Applications, 1987, 21:2, 126–142

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UDC: 517.9
Received: 14.11.1986

Citation: I. M. Krichever, S. P. Novikov, “Algebras of virasoro type, riemann surfaces and structures of the theory of solitons”, Funktsional. Anal. i Prilozhen., 21:2 (1987), 46–63; Funct. Anal. Appl., 21:2 (1987), 126–142

Citation in format AMSBIB
\by I.~M.~Krichever, S.~P.~Novikov
\paper Algebras of virasoro type, riemann surfaces and structures of the theory of solitons
\jour Funktsional. Anal. i Prilozhen.
\yr 1987
\vol 21
\issue 2
\pages 46--63
\jour Funct. Anal. Appl.
\yr 1987
\vol 21
\issue 2
\pages 126--142

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    This publication is cited in the following articles:
    1. I. M. Krichever, S. P. Novikov, “Virasoro-type algebras, Riemann surfaces and strings in Minkowsky space”, Funct. Anal. Appl., 21:4 (1987), 294–307  mathnet  crossref  mathscinet  zmath  isi
    2. Yu. A. Neretin, “Holomorphic extensions of representations of the group of the diffeomorphisms of the circle”, Math. USSR-Sb., 67:1 (1990), 75–97  mathnet  crossref  mathscinet  zmath  isi
    3. O. I. Bogoyavlenskii, “Overturning solitons in new two-dimensional integrable equations”, Math. USSR-Izv., 34:2 (1990), 245–259  mathnet  crossref  mathscinet  zmath
    4. I. M. Krichever, “Spectral theory of two-dimensional periodic operators and its applications”, Russian Math. Surveys, 44:2 (1989), 145–225  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. I. M. Krichever, S. P. Novikov, “Algebras of virasoro type, energy-momentum tensor, and decomposition operators on Riemann surfaces”, Funct. Anal. Appl., 23:1 (1989), 19–33  mathnet  crossref  mathscinet  zmath  isi
    6. O. K. Sheinman, “Hamiltonian string formalism and discrete groups”, Funct. Anal. Appl., 23:2 (1989), 124–128  mathnet  crossref  mathscinet  zmath  isi
    7. Yu. A. Neretin, “A spinor representation of an infinite-dimensional orthogonal semigroup and the virasoro algebra”, Funct. Anal. Appl., 23:3 (1989), 196–207  mathnet  crossref  mathscinet  zmath  isi
    8. A. V. Zabrodin, “Fermions on a Riemann surface and the Kadomtsev–Petviashvili equation”, Theoret. and Math. Phys., 78:2 (1989), 167–177  mathnet  crossref  mathscinet  zmath  isi
    9. P. G. Grinevich, A. Yu. Orlov, “Variations of the complex structure of Riemann surfaces by vector fields on a contour and objects of the KP theory. The Krichever–Novikov problem of the action on the Baker–Akhieser functions”, Funct. Anal. Appl., 24:1 (1991), 61–63  mathnet  crossref  mathscinet  zmath  isi
    10. O. K. Sheinman, “Elliptic affine Lie algebras”, Funct. Anal. Appl., 24:3 (1990), 210–219  mathnet  crossref  mathscinet  zmath  isi
    11. S. P. Novikov, “Quantization of finite-gap potentials and nonlinear quasiclassical approximation in nonperturbative string theory”, Funct. Anal. Appl., 24:4 (1990), 296–306  mathnet  crossref  mathscinet  zmath  isi
    12. F. F. Voronov, “Characteristic classes of infinite-dimensional vector bundles”, Russian Math. Surveys, 46:3 (1991), 238–240  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    13. O. K. Sheinman, “Highest weight modules over certain quasigraded Lie algebras on elliptic curves”, Funct. Anal. Appl., 26:3 (1992), 203–208  mathnet  crossref  mathscinet  zmath  isi
    14. O. K. Sheinman, “Affine Lie Algebras on Riemann Surfaces”, Funct. Anal. Appl., 27:4 (1993), 266–272  mathnet  crossref  mathscinet  zmath  isi
    15. O. K. Sheinman, “Weil Modules with Highest Weight for Affine Lie Algebras on Riemann Surfaces”, Funct. Anal. Appl., 29:1 (1995), 44–55  mathnet  crossref  mathscinet  zmath  isi
    16. O. K. Sheinman, “The Krichever–Novikov algebras and CCC-groups”, Russian Math. Surveys, 50:5 (1995), 1097–1099  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    17. A. N. Varchenko, G. Felder, “Algebraic Integrability of the Two-Body Ruijsenaars Operator”, Funct. Anal. Appl., 32:2 (1998), 81–92  mathnet  crossref  crossref  mathscinet  zmath  isi
    18. M. Schlichenmaier, O. K. Sheinman, “Wess–Zumino–Witten–Novikov theory, Knizhnik–Zamolodchikov equations, and Krichever–Novikov algebras”, Russian Math. Surveys, 54:1 (1999), 213–249  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    19. Zabrodin, A, “On the spectral curve of the difference Lame operator”, International Mathematics Research Notices, 1999, no. 11, 589  isi
    20. I. M. Krichever, S. P. Novikov, “Holomorphic bundles and commuting difference operators. Two-point constructions”, Russian Math. Surveys, 55:3 (2000), 586–588  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    21. O. K. Sheinman, “The Fermion Model of Representations of Affine Krichever–Novikov Algebras”, Funct. Anal. Appl., 35:3 (2001), 209–219  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    22. O. K. Sheinman, “Second-order Casimir operators for the affine Krichever–Novikov algebras $\widehat{\mathfrak{gl}}_{g,2}$ and $\widehat{\mathfrak{sl}}_{g,2}$”, Russian Math. Surveys, 56:5 (2001), 986–987  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    23. O. K. Sheinman, “Second order Casimirs for the affine Krichever–Novikov algebras $\widehat{\mathfrak{gl}}_{g,2}$ and $\widehat{\mathfrak{sl}}_{g,2}$”, Mosc. Math. J., 1:4 (2001), 605–628  mathnet  crossref  mathscinet  zmath
    24. I. M. Krichever, S. P. Novikov, “Two-dimensionalized Toda lattice, commuting difference operators, and holomorphic bundles”, Russian Math. Surveys, 58:3 (2003), 473–510  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    25. M. Schlichenmaier, “Higher genus affine algebras of Krichever–Novikov type”, Mosc. Math. J., 3:4 (2003), 1395–1427  mathnet  crossref  mathscinet  zmath
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    27. Skrypnyk, T, “Deformations of loop algebras and classical integrable systems: Finite-dimensional Hamiltonian systems”, Reviews in Mathematical Physics, 16:7 (2004), 823  crossref  isi
    28. V. M. Buchstaber, D. V. Leikin, “Addition Laws on Jacobian Varieties of Plane Algebraic Curves”, Proc. Steklov Inst. Math., 251 (2005), 49–120  mathnet  mathscinet  zmath
    29. O. K. Sheinman, “Projective Flat Connections on Moduli Spaces of Riemann Surfaces and the Knizhnik–Zamolodchikov Equations”, Proc. Steklov Inst. Math., 251 (2005), 293–304  mathnet  mathscinet  zmath
    30. T. V. Skrypnik, “Quasigraded lie algebras, Kostant–Adler scheme, and integrable hierarchies”, Theoret. and Math. Phys., 142:2 (2005), 275–288  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
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    32. Skrypnyk, T, “New integrable Gaudin-type systems, classical r-matrices and quasigraded Lie algebras”, Physics Letters A, 334:5–6 (2005), 390  crossref  isi
    33. Sheinman O.K., “Krichever-Novikov algebras and their representations”, Noncommutative Geometry and Representation Theory in Mathematical Physics, Contemporary Mathematics Series, 391, 2005, 313–321  crossref  isi
    34. V. M. Buchstaber, I. M. Krichever, “Integrable equations, addition theorems, and the Riemann–Schottky problem”, Russian Math. Surveys, 61:1 (2006), 19–78  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    35. L. O. Sheinman, “Sigma-functions and Krichever–Novikov bases”, Russian Math. Surveys, 61:6 (2006), 1183–1185  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    36. Taras V. Skrypnyk, “Quasigraded Lie Algebras and Modified Toda Field Equations”, SIGMA, 2 (2006), 043, 14 pp.  mathnet  crossref  mathscinet  zmath
    37. Skrypnyk, T, “Integrable quantum spin chains, non-skew symmetric r-matrices and quasigraded Lie algebras”, Journal of Geometry and Physics, 57:1 (2006), 53  crossref  isi
    38. Skrypnyk, T, “Modified non-Abelian Toda field equations and twisted quasigraded Lie algebras”, Journal of Mathematical Physics, 47:6 (2006), 063509  crossref  isi
    39. Skrypnyk, T, “Integrable deformations of the mKdV and SG hierarchies and quasigraded Lie algebras”, Physica D-Nonlinear Phenomena, 216:2 (2006), 247  crossref  isi
    40. Alice Fialowski, Marc de Montigny, “On Deformations and Contractions of Lie Algebras”, SIGMA, 2 (2006), 048, 10 pp.  mathnet  crossref  mathscinet  zmath
    41. O. K. Sheinman, “Krichever–Novikov Algebras, their Representations and Applications in Geometry and Mathematical Physics”, Proc. Steklov Inst. Math., 274, suppl. 1 (2011), S85–S161  mathnet  crossref  crossref  zmath
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    49. Alexandrov, A, “BGWM as second constituent of complex matrix model”, Journal of High Energy Physics, 2009, no. 12, 053
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  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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