DRINFELD-TYPE PRESENTATIONS OF LOOP ALGEBRAS

Let g be the derived subalgebra of a Kac-Moody Lie algebra of finite-type or affine-type, let mu be a diagram automorphism of g, and let L(g, mu) be the loop algebra of g associated to mu. In this paper, by using the vertex algebra technique, we provide a general construction of current-type presentations for the universal central extension (g) over cap[mu] of L( g, mu). The construction contains the classical limit of Drinfeld's new realization for (twisted and untwisted) quantum affine algebras [Soviet Math. Dokl. 36 (1988), pp. 212-216] and the Moody-Rao-Yokonuma presentation for toroidal Lie algebras [Geom. Dedicata 35 (1990), pp. 283-307] as special examples. As an application, when g is of simply-laced-type, we prove that the classical limit of the mu-twisted quantum affinization of the quantum Kac-Moody algebra associated to g introduced in [J. Math. Phys. 59 (2018), 081701] is the universal enveloping algebra of (g) over cap [mu].