XXVII Workshop on Geometric Methods in Physics 29.06-05.07.2008

Martin Schlichenmaier

Almost-graded central extensions of Lax operator algebras

Lax operator algebras constitute a new class of infinite dimensional Lie algebras of geometric origin. More precisely, they are algebras of matrices whose entries are meromorphic functions on a compact Riemann surface. They generalize classical current algebras and current algebras of Krichever-Novikov type. Lax operators for gl(n) were introduced by Krichever. In joint works of Krichever and Sheinman their algebraic structures was revealed and extended to more general groups. These algebras are almost-graded. In this talk we recall their definition and present classification and uniqueness results for almost-graded central extensions for this new class of algebras. The presented results are joint work with Oleg Sheinman.