Central extensions of Lax operator algebras

Details Central extensions of Lax operator algebras Central extensions of Lax operator algebras

2007-11-29

arxiv.org/abs/0711.4688v1

Russian Math. Surveys 63:4 (2008) 727--766

Mathematics

Quantum Algebra

43 pages

Scientific paper

10.1070/RM2008v063n04ABEH004550

Lax operator algebras were introduced by Krichever and Sheinman as a further development of I.Krichever's theory of Lax operators on algebraic curves. These are almost-graded Lie algebras of current type. In this article local cocycles and associated almost-graded central extensions are classified. It is shown that in the case that 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.

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