Almost-graded central extensions of Lax operator algebras

Martin Schlichenmaier. "Almost-graded central extensions of Lax operator algebras." Banach Center Publications 93.1 (2011): 129-144. <http://eudml.org/doc/282189>.

@article{MartinSchlichenmaier2011,
abstract = {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.},
author = {Martin Schlichenmaier},
journal = {Banach Center Publications},
keywords = {Lie algebras of current type; local cocycles; central extensions; Krichever-Novikov type algebras; Tyurin parameters},
language = {eng},
number = {1},
pages = {129-144},
title = {Almost-graded central extensions of Lax operator algebras},
url = {http://eudml.org/doc/282189},
volume = {93},
year = {2011},
}

TY - JOUR
AU - Martin Schlichenmaier
TI - Almost-graded central extensions of Lax operator algebras
JO - Banach Center Publications
PY - 2011
VL - 93
IS - 1
SP - 129
EP - 144
AB - 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.
LA - eng
KW - Lie algebras of current type; local cocycles; central extensions; Krichever-Novikov type algebras; Tyurin parameters
UR - http://eudml.org/doc/282189
ER -