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 \widehat{W}_1 of W_1 and the corresponding loop algebra M of \widehat{W}_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
Avitabile, M. (2005). The other graded Lie algebra associated to the Nottingham group. COMMUNICATIONS IN ALGEBRA, 33(3), 775-791 [10.1081/AGB-200051135].
The other graded Lie algebra associated to the Nottingham group
AVITABILE, MARINA
2005
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 \widehat{W}_1 of W_1 and the corresponding loop algebra M of \widehat{W}_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
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