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Classification of central extension of Lax operator algebras. (English) Zbl 1166.81333
Kielanowski, Piotr (ed.) et al., Geometric methods in physics. Proceedings of the xxvii workshop on geometric methods in physics, Białowieża, Poland, 29 June – 5 July 2008. Melville, NY: American Institute of Physics (AIP) (ISBN 978-0-7354-0610-0/hbk). AIP Conference Proceedings 1079, 227-234 (2008).
Summary: 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.
For the entire collection see [Zbl 1157.81001].
81R05 Finite-dimensional groups and algebras motivated by physics and their representations
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
22E70 Applications of Lie groups to the sciences; explicit representations