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This article is cited in 64 scientific papers (total in 64 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
\pages 46--63
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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
-
O. I. Bogoyavlenskii, “Overturning solitons in new two-dimensional integrable equations”, Math. USSR-Izv., 34:2 (1990), 245–259
-
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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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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-
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-
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-
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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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-
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-
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-
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-
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-
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-
M. Schlichenmaier, “Multipoint Lax operator algebras: almost-graded structure and central extensions”, Sb. Math., 205:5 (2014), 722–762
-
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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-
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-
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-
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-
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-
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