Lax Operator Algebras

In this paper we develop a general concept of Lax operators on algebraic curves introduced in [I. M. Krichever, Comm. Math. Phys., 229, 2 (2002), 229–269]. We observe that the space of Lax operators is closed with respect to their usual multiplication as matrix-valued functions. We construct the orthogonal and symplectic analogs of Lax operators, prove that they constitute almost graded Lie algebras and construct local central extensions of those Lie algebras.