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Uspekhi Mat. Nauk, 2008, Volume 63, Issue 4(382), Pages 131–172 (Mi umn9221)  

This article is cited in 9 scientific papers (total in 9 papers)

Central extensions of Lax operator algebras

M. Schlichenmaiera, O. K. Sheinmanb

a University of Luxembourg
b Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: Lax operator algebras were introduced by Krichever and Sheinman as a further development of Krichever's theory of Lax operators on algebraic curves. These are almost-graded Lie algebras of current type. In this paper local cocycles and associated almost-graded central extensions of Lax operator algebras are classified. It is shown that in the case when the corresponding finite-dimensional Lie algebra is simple the two-cohomology space is one-dimensional. An important role is played by the action of the Lie algebra of meromorphic vector fields on the Lax operator algebra via suitable covariant derivatives.

DOI: https://doi.org/10.4213/rm9221

Full text: PDF file (816 kB)
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English version:
Russian Mathematical Surveys, 2008, 63:4, 727–766

Bibliographic databases:

Document Type: Article
UDC: 517.9
MSC: 17B65, 17B67, 17B80, 14H55, 14H70, 30F30, 81R10, 81T40
Received: 16.06.2008

Citation: M. Schlichenmaier, O. K. Sheinman, “Central extensions of Lax operator algebras”, Uspekhi Mat. Nauk, 63:4(382) (2008), 131–172; Russian Math. Surveys, 63:4 (2008), 727–766

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
    2. O. K. Sheinman, “Lax operator algebras of type G 2”, Dokl. Math, 89:2 (2014), 151  mathnet  crossref  mathscinet  zmath  isi  scopus
    3. 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
    4. O. K. Sheinman, “Lax operators algebras and gradings on semisimple Lie algebras”, Dokl. Math, 91:2 (2015), 160  mathnet  crossref  mathscinet  zmath  isi  scopus
    5. 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
    6. 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
    7. Oleg K. Sheinman, “Global current algebras and localization on Riemann surfaces”, Mosc. Math. J., 15:4 (2015), 833–846  mathnet  mathscinet  zmath  elib
    8. 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
    9. 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
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