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), with the spectral parameter on a Riemann surface, were introduced by Krichever. In joint works of Krichever and Sheinman their algebraic structure was revealed and extended to more general groups. These algebras are almost-graded. In this article their definition is recalled and classification and uniqueness results for almost-graded central extensions for this new class of algebras are presented. The explicit forms of the defining cocycles are given. If the finite-dimensional Lie algebra on which the Lax operator algebra is based is simple then, up to equivalence and rescaling of the central element, there is a unique non-trivial almost-graded central extension. Some results are joint work with Oleg Sheinman.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc93-0-11,
author = {Martin Schlichenmaier},
title = {Almost-graded central extensions of Lax operator algebras},
journal = {Banach Center Publications},
volume = {95},
year = {2011},
pages = {129-144},
zbl = {1275.17045},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc93-0-11}
}
Martin Schlichenmaier. Almost-graded central extensions of Lax operator algebras. Banach Center Publications, Tome 95 (2011) pp. 129-144. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc93-0-11/