Classical elliptic current algebras
Quantum Algebra
2007-09-25 v1
Abstract
In this paper we discuss classical elliptic current algebras and show that there are two different choices of commutative test function algebras on a complex torus leading to two different elliptic current algebras. Quantization of these classical current algebras give rise to two classes of quantized dynamical quasi-Hopf current algebras studied by Enriquez-Felder-Rubtsov and Arnaudon-Buffenoir-Ragoucy-Roche-Jimbo-Konno-Odake-Shiraishi. Different degenerations of the classical elliptic algebras are considered. They yield different versions of rational and trigonometric current algebras. We also review the averaging method of Faddeev-Reshetikhin, which allows to restore elliptic algebras from the trigonometric ones.
Cite
@article{arxiv.0709.3592,
title = {Classical elliptic current algebras},
author = {S. Pakuliak and V. Rubtsov and A. Silantyev},
journal= {arXiv preprint arXiv:0709.3592},
year = {2007}
}