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arXiv · 0709.3592

Classical elliptic current algebras

S. Pakuliak·V. Rubtsov·A. Silantyev
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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.

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BibTeXRIS

S. Pakuliak, V. Rubtsov, A. Silantyev. 2007-09-22. Classical elliptic current algebras. https://arxiv.org/abs/0709.3592

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