Central extensions of gauge groups revisited

Abstract. We present an explicit construction for the central extension of the group Map(X, G) where X is a compact manifold and G is a Lie group. If X is a complex curve we obtain a simple construction of the extension by the Picard variety Pic(X). The construction is easily adapted to the extension of Aut(E), the gauge group of automorphisms of a nontrivial vector bundle E.