Abstract
Lax operator algebras were introduced by Krichever and Sheinman as further developments of Krichever’s theory of Lax operators on algebraic curves. They are infinite dimensional Lie algebras of current type with meromorphic objects on compact Riemann surfaces (resp. algebraic curves) as elements. Here we report on joint work with Oleg Sheinman on the classification of their almost‐graded central extensions. It turns out that in case that the finite‐dimensional Lie algebra on which the Lax operator algebra is based on is simple there is a unique almost‐graded central extension up to equivalence and rescaling of the central element.
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