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Proceedings of the Steklov Institute of Mathematics

, Volume 263, Issue 1, pp 204–213 | Cite as

Lax operator algebras and integrable hierarchies

  • O. K. SheinmanEmail author
Article

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.

Keywords

Riemann Surface STEKLOV Institute Central Extension Algebraic Curf Holomorphic Vector Bundle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Pleiades Publishing, Ltd. 2008

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteMoscowRussia
  2. 2.Independent University of MoscowMoscowRussia

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