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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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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
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\paper Algebras of virasoro type, riemann surfaces and structures of the theory of solitons
\jour Funktsional. Anal. i Prilozhen.
\yr 1987
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\issue 2
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\jour Funct. Anal. Appl.
\yr 1987
\vol 21
\issue 2
\pages 126--142
\crossref{https://doi.org/10.1007/BF01078026}
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I. M. Krichever, S. P. Novikov, “Virasoro-type algebras, Riemann surfaces and strings in Minkowsky space”, Funct. Anal. Appl., 21:4 (1987), 294–307
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Yu. A. Neretin, “Holomorphic extensions of representations of the group of the diffeomorphisms of the circle”, Math. USSR-Sb., 67:1 (1990), 75–97
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O. I. Bogoyavlenskii, “Overturning solitons in new two-dimensional integrable equations”, Math. USSR-Izv., 34:2 (1990), 245–259
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I. M. Krichever, “Spectral theory of two-dimensional periodic operators and its applications”, Russian Math. Surveys, 44:2 (1989), 145–225
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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
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O. K. Sheinman, “Hamiltonian string formalism and discrete groups”, Funct. Anal. Appl., 23:2 (1989), 124–128
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Yu. A. Neretin, “A spinor representation of an infinite-dimensional orthogonal semigroup and the virasoro algebra”, Funct. Anal. Appl., 23:3 (1989), 196–207
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A. V. Zabrodin, “Fermions on a Riemann surface and the Kadomtsev–Petviashvili equation”, Theoret. and Math. Phys., 78:2 (1989), 167–177
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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
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O. K. Sheinman, “Elliptic affine Lie algebras”, Funct. Anal. Appl., 24:3 (1990), 210–219
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S. P. Novikov, “Quantization of finite-gap potentials and nonlinear quasiclassical approximation in nonperturbative string theory”, Funct. Anal. Appl., 24:4 (1990), 296–306
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F. F. Voronov, “Characteristic classes of infinite-dimensional vector bundles”, Russian Math. Surveys, 46:3 (1991), 238–240
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O. K. Sheinman, “Highest weight modules over certain quasigraded Lie algebras on elliptic curves”, Funct. Anal. Appl., 26:3 (1992), 203–208
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O. K. Sheinman, “Affine Lie Algebras on Riemann Surfaces”, Funct. Anal. Appl., 27:4 (1993), 266–272
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O. K. Sheinman, “Weil Modules with Highest Weight for Affine Lie Algebras on Riemann Surfaces”, Funct. Anal. Appl., 29:1 (1995), 44–55
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O. K. Sheinman, “The Krichever–Novikov algebras and CCC-groups”, Russian Math. Surveys, 50:5 (1995), 1097–1099
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A. N. Varchenko, G. Felder, “Algebraic Integrability of the Two-Body Ruijsenaars Operator”, Funct. Anal. Appl., 32:2 (1998), 81–92
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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
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Zabrodin, A, “On the spectral curve of the difference Lame operator”, International Mathematics Research Notices, 1999, no. 11, 589
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I. M. Krichever, S. P. Novikov, “Holomorphic bundles and commuting difference operators. Two-point constructions”, Russian Math. Surveys, 55:3 (2000), 586–588
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O. K. Sheinman, “The Fermion Model of Representations of Affine Krichever–Novikov Algebras”, Funct. Anal. Appl., 35:3 (2001), 209–219
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O. K. Sheinman, “Second-order Casimir operators for the affine Krichever–Novikov algebras
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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
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I. M. Krichever, S. P. Novikov, “Two-dimensionalized Toda lattice, commuting difference operators, and holomorphic bundles”, Russian Math. Surveys, 58:3 (2003), 473–510
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M. Schlichenmaier, “Higher genus affine algebras of Krichever–Novikov type”, Mosc. Math. J., 3:4 (2003), 1395–1427
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M. Schlichenmaier, O. K. Sheinman, “Knizhnik–Zamolodchikov equations for positive genus and Krichever–Novikov algebras”, Russian Math. Surveys, 59:4 (2004), 737–770
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Skrypnyk, T, “Deformations of loop algebras and classical integrable systems: Finite-dimensional Hamiltonian systems”, Reviews in Mathematical Physics, 16:7 (2004), 823
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V. M. Buchstaber, D. V. Leikin, “Addition Laws on Jacobian Varieties of Plane Algebraic Curves”, Proc. Steklov Inst. Math., 251 (2005), 49–120
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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
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T. V. Skrypnik, “Quasigraded lie algebras, Kostant–Adler scheme, and integrable hierarchies”, Theoret. and Math. Phys., 142:2 (2005), 275–288
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O. K. Sheinman, “Highest weight representations of Krichever–Novikov algebras and integrable systems”, Russian Math. Surveys, 60:2 (2005), 370–372
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Skrypnyk, T, “New integrable Gaudin-type systems, classical r-matrices and quasigraded Lie algebras”, Physics Letters A, 334:5–6 (2005), 390
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Sheinman O.K., “Krichever-Novikov algebras and their representations”, Noncommutative Geometry and Representation Theory in Mathematical Physics, Contemporary Mathematics Series, 391, 2005, 313–321
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V. M. Buchstaber, I. M. Krichever, “Integrable equations, addition theorems, and the Riemann–Schottky problem”, Russian Math. Surveys, 61:1 (2006), 19–78
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L. O. Sheinman, “Sigma-functions and Krichever–Novikov bases”, Russian Math. Surveys, 61:6 (2006), 1183–1185
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Skrypnyk, T, “Integrable quantum spin chains, non-skew symmetric r-matrices and quasigraded Lie algebras”, Journal of Geometry and Physics, 57:1 (2006), 53
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Skrypnyk, T, “Modified non-Abelian Toda field equations and twisted quasigraded Lie algebras”, Journal of Mathematical Physics, 47:6 (2006), 063509
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Alice Fialowski, Marc de Montigny, “On Deformations and Contractions of Lie Algebras”, SIGMA, 2 (2006), 048, 10 pp.
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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
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A. S. Alexandrov, A. D. Mironov, A. Yu. Morozov, “$M$-Theory of Matrix Models”, Theoret. and Math. Phys., 150:2 (2007), 153–164
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Schlichenmaier M., “A global operator approach to Wess-Zumino-Novikov-Witten models”, XXVI Workshop on Geometrical Methods in Physics, AIP Conference Proceedings, 956, 2007, 107–119
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Alexandrov A., Mironov A., Morozov A., “BGWM as second constituent of complex matrix model”, Journal of High Energy Physics, 2009, no. 12, 053
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J. Harnad, V. Z. Enolski, “Schur function expansions of KP $\tau$-functions associated to algebraic curves”, Russian Math. Surveys, 66:4 (2011), 767–807
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B. O. Vasilevskiǐ, “The Green's function of a five-point discretization of a two-dimensional finite-gap Schrödinger operator: The case of four singular points on the spectral curve”, Siberian Math. J., 54:6 (2013), 994–1004
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M. Schlichenmaier, “Multipoint Lax operator algebras: almost-graded structure and central extensions”, Sb. Math., 205:5 (2014), 722–762
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Skrypnyk T., “Decompositions of Quasigraded Lie Algebras, Non-Skew-Symmetric Classical R-Matrices and Generalized Gaudin Models”, J. Geom. Phys., 75 (2014), 98–112
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Proc. Steklov Inst. Math., 286 (2014), 240–252
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Sheinman O.K., “Lax Operator Algebras of Type $G_2$”, Dokl. Math., 89:2 (2014), 151–153
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B. O. Vasilevskii, “The Green Function of the Discrete Finite-Gap One-Energy Two-Dimensional Schrödinger Operator on the Quad Graph”, Math. Notes, 98:1 (2015), 38–52
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Oleg K. Sheinman, “Global current algebras and localization on Riemann surfaces”, Mosc. Math. J., 15:4 (2015), 833–846
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