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 wordsLax operator current algebra Tyurin data almost graded structure local central extension
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- O. K. Sheinman, “Affine Krichever-Novikov algebras, their representations and applications,” in: Geometry, Topology and Mathematical Physics. S. P. Novikov’s Seminar 2002–2003, Amer. Soc. Transl. (2), vol. 212 (eds. V. M. Buchstaber, I. M. Krichever), Amer. Math. Soc., Providence, R.I., 2004, 297–316; http://arxiv.org/abs/Math.RT/0304020.Google Scholar