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
The presented results are joint work
with Oleg Sheinman.