Functional Analysis and Its Applications

, Volume 41, Issue 4, pp 284–294 | Cite as

Lax operator algebras

  • I. M. Krichever
  • O. K. Sheinman


In this paper, we develop the general approach, introduced in [l], to Lax operators on algebraic curves. We observe that the space of Lax operators is closed with respect to their usual multiplication as matrix-valued functions. We construct orthogonal and symplectic analogs of Lax operators, prove that they form almost graded Lie algebras, and construct local central extensions of these Lie algebras.

Key words

Lax operator current algebra Tyurin data almost graded structure local central extension 


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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.Landau Institute for Theoretical PhysicsUSA
  2. 2.Columbia University
  3. 3.Steklov Mathematical InstituteRussia
  4. 4.Independent University of MoscowMoscow

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