The other graded Lie algebra associated to the Nottingham group

摘要

The graded Lie algebra L associated to the Nottingham group with respect to its natural filtration is known to be a loop algebra of the first Witt algebra W-1. The fact that the Schur multiplier of W-1, in characteristic p > 3, is one-dimensional implies that L is not finitely presented. Consider the universal covering (W) over cap (1) of W-1 and the corresponding loop algebra M of (W) over cap (1). In this paper we prove that M itself is finitely presented for p > 3. In characteristic p > 11 the algebra M turns out to be presented by two relations.