ABSTRACT
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 Ŵ 1 of W 1 and the corresponding loop algebra M of Ŵ 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.
ACKNOWLEDGMENT
The author is grateful to A. Caranti for suggesting the problem and to A. Caranti, N. Gavioli, S. Mattarei, and C. M. Scoppola for several useful discussions.
Notes
Communicated by E. Zelmanov.
‡The author is a member of INdAm-GNSAGA; Italy.