Central extensions of Lax operator algebras

Lax operator algebras were introduced by Krichever and Shein-man as a further development of Krichever's theory of Lax operators oil algebraic curves. These are almost-graded Lie algebras of current type. In this paper local cocycles and associated almost-graded central extensions of Lax operator algebras are classified. It is shown that in the case when the corresponding finite-dimensional Lie algebra, is simple the two-cohomology space is one-dimensional. An important role is Played by the action of the Lie algebra of meromorphic vector fields on the Lax operator algebra via suitable covariant derivatives.