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Tr. Mat. Inst. Steklova, 2008, Volume 263, Pages 216–226 (Mi tm793)  

This article is cited in 1 scientific paper (total in 1 paper)

Lax Operator Algebras and Integrable Hierarchies

O. K. Sheinmanab

a Steklov Mathematical Institute, Russian Academy of Sciences
b Independent University of Moscow

Abstract: We study applications of a new class of infinite-dimensional Lie algebras, called Lax operator algebras, which goes back to the works by I. Krichever and S. Novikov on finite-zone integration related to holomorphic vector bundles and on Lie algebras on Riemann surfaces. Lax operator algebras are almost graded Lie algebras of current type. They were introduced by I. Krichever and the author as a development of the theory of Lax operators on Riemann surfaces due to I. Krichever, and further investigated in a joint paper by M. Schlichenmaier and the author. In this article we construct integrable hierarchies of Lax equations of that type.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2008, 263, 204–213

Bibliographic databases:

UDC: 512.554.32
Received in July 2008

Citation: O. K. Sheinman, “Lax Operator Algebras and Integrable Hierarchies”, Geometry, topology, and mathematical physics. I, Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 70th birthday, Tr. Mat. Inst. Steklova, 263, MAIK Nauka/Interperiodica, Moscow, 2008, 216–226; Proc. Steklov Inst. Math., 263 (2008), 204–213

Citation in format AMSBIB
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\paper Lax Operator Algebras and Integrable Hierarchies
\inbook Geometry, topology, and mathematical physics.~I
\bookinfo Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 70th birthday
\serial Tr. Mat. Inst. Steklova
\yr 2008
\vol 263
\pages 216--226
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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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
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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