The Lie algebra of sl(2)-valued automorphic functions on a torus

Abstract

It is shown that the Lie algebra of the automorphic, meromorphic sl(2, C) -valued functions on a torus is a geometric realization of a certain infinite-dimensional finitely generated Lie algebra. In the trigonometric limit, when the modular parameter of the torus goes to zero, the former Lie algebra goes over into the sl(2,C) -valued loop algebra, while the latter one - into the Lie algebra (sl(2)^)'/(centre) .