Presenting the graded Lie algebra associated to the Nottingham group

The graded Lie algebra L associated to the Nottingham group is a loop algebra of the Witt algebra W-1. The universal covering <(W) over cap>(1) of W-1 has one-dimensional centre, so that the corresponding loop algebra M of <(W) over cap>(1) has an infinite-dimensional centre Z(M). As M/Z(M) is isomorphic to L, it follows from a result of B. H. Neumann that L is not finitely presented. However, we are able to show that M itself is finitely presented. We work more generally with the Zassenhaus algebras W-n. In the group context, examples of finitely presented groups whose centre is not finitely generated were given by V. N. Remeslennikov and H. Abels. (C) 1997 Academic Press.