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Funktsional. Anal. i Prilozhen., 2007, Volume 41, Issue 4, Pages 46–59 (Mi faa2878)  

This article is cited in 13 scientific papers (total in 13 papers)

Lax Operator Algebras

I. M. Kricheverab, O. K. Sheinmancd

a L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
b Columbia University
c Steklov Mathematical Institute, Russian Academy of Sciences
d Independent University of Moscow

Abstract: In this paper we develop a general concept of Lax operators on algebraic curves introduced in [I. M. Krichever, Comm. Math. Phys., 229, 2 (2002), 229–269]. We observe that the space of Lax operators is closed with respect to their usual multiplication as matrix-valued functions. We construct the orthogonal and symplectic analogs of Lax operators, prove that they constitute almost graded Lie algebras and construct local central extensions of those Lie algebras.

Keywords: Lax operators, current algebras, Tyurin data, almost graded structure, local central extension

DOI: https://doi.org/10.4213/faa2878

Full text: PDF file (220 kB)
References: PDF file   HTML file

English version:
Functional Analysis and Its Applications, 2007, 41:4, 284–294

Bibliographic databases:

UDC: 917.9
Received: 28.02.2007

Citation: I. M. Krichever, O. K. Sheinman, “Lax Operator Algebras”, Funktsional. Anal. i Prilozhen., 41:4 (2007), 46–59; Funct. Anal. Appl., 41:4 (2007), 284–294

Citation in format AMSBIB
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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. M. Schlichenmaier, O. K. Sheinman, “Central extensions of Lax operator algebras”, Russian Math. Surveys, 63:4 (2008), 727–766  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. O. K. Sheinman, “Lax Operator Algebras and Integrable Hierarchies”, Proc. Steklov Inst. Math., 263 (2008), 204–213  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    3. O. K. Sheinman, “Lax operator algebras and Hamiltonian integrable hierarchies”, Russian Math. Surveys, 66:1 (2011), 145–171  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. M. Schlichenmaier, “Multipoint Lax operator algebras: almost-graded structure and central extensions”, Sb. Math., 205:5 (2014), 722–762  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. Sheinman O.K., “Lax Operator Algebras of Type $G_2$”, Dokl. Math., 89:2 (2014), 151–153  mathnet  crossref  mathscinet  zmath  isi  scopus
    6. O. K. Sheinman, “Semisimple Lie algebras and Hamiltonian theory of finite-dimensional Lax equations with spectral parameter on a Riemann surface”, Proc. Steklov Inst. Math., 290:1 (2015), 178–188  mathnet  crossref  crossref  isi  elib  elib
    7. O. K. Sheinman, “Hierarchies of finite-dimensional Lax equations with a spectral parameter on a Riemann surface and semisimple Lie algebras”, Theoret. and Math. Phys., 185:3 (2015), 1816–1831  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    8. Oleg K. Sheinman, “Global current algebras and localization on Riemann surfaces”, Mosc. Math. J., 15:4 (2015), 833–846  mathnet  mathscinet  zmath  elib
    9. Sheinman O.K., “Lax Operators Algebras and Gradings on Semisimple Lie Algebras”, Dokl. Math., 91:2 (2015), 160–162  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    10. O. K. Sheinman, “Lax operator algebras and integrable systems”, Russian Math. Surveys, 71:1 (2016), 109–156  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    11. Sheinman O.K., “Lax Operator Algebras and Gradings on Semi-Simple Lie Algebras”, Transform. Groups, 21:1 (2016), 181–196  crossref  mathscinet  zmath  isi  scopus
    12. Chalykh O., Fairon M., “Multiplicative Quiver Varieties and Generalised Ruijsenaars-Schneider Models”, J. Geom. Phys., 121 (2017), 413–437  crossref  mathscinet  zmath  isi  scopus
    13. O. K. Sheinman, “Matrix divisors on Riemann surfaces and Lax operator algebras”, Trans. Moscow Math. Soc., 78 (2017), 109–121  mathnet  crossref  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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