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Presenting the Graded Lie Algebra Associated to the Nottingham Group

✍ Scribed by A. Caranti

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
273 KB
Volume
198
Category
Article
ISSN
0021-8693

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✦ Synopsis

The graded Lie algebra L associated to the Nottingham group is a loop algebra Γ΄f the Witt algebra W . The universal covering W of W has one-dimensional 1 1 1 Δ‰entre, so that the corresponding loop algebra M of W has an infinite-dimen-1 Ε½ . Ε½ . sional centre Z M . As MrZ 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 . In the group context, n examples of finitely presented groups whose centre is not finitely generated were given by V. N. Remeslennikov and H. Abels.

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In our previous work (math/0008128), we studied the set Quant(K) of all universal quantization functors of Lie bialgebras over a field K of characteristic zero, compatible with the operations of taking duals and doubles. We showed that Quant ), where G 0 (K) is a universal group and Q Q(K) is a quot