Classification of central extensions of Lax operator algebras

Journal Article · Tue Nov 18 00:00:00 EST 2008 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.3043863· OSTI ID:21254873

Schlichenmaier, Martin ^[1]

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1. University of Luxembourg, Mathematics Research Unit, Campus Limpertsberg 162 Avenue de la Faiencerie, L-1511 Luxembourg (Luxembourg)

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.

• OSTI ID: 21254873
• Journal Information: AIP Conference Proceedings, Vol. 1079, Issue 1; Conference: 27. workshop on geometric methods in physics, Bialowieza (Poland), 29 Jun - 5 Jul 2008; Other Information: DOI: 10.1063/1.3043863; (c) 2008 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
CLASSIFICATION
LAX THEOREM
LIE GROUPS
RIEMANN SHEET