Drinfeld-type presentations of loop algebras

Abstract

Let g be the derived subalgebra of a Kac-Moody Lie algebra of finite type or affine type, µ a diagram automorphism of g and L(g, µ) the loop algebra of g associated to µ. In this paper, by using the vertex algebra technique, we provide a general construction of current type presentations for the universal central extension g[µ] of L(g, µ). The construction contains the classical limit of Drinfeld's new realization for (twisted and untwisted) quantum affine algebras ([Dr]) and the Moody-Rao-Yokonuma presentation for toroidal Lie algebras ([MRY]) as special examples. As an application, when g is of simply-laced type, we prove that the classical limit of the µ-twisted quantum affinization of the quantum Kac-Moody algebra associated to g introduced in [CJKT1] is the universal enveloping algebra of g [µ].