  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.

Quantum Algebra