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Journal of Lie Theory 21 (2011), No. 1, 071--078
Copyright Heldermann Verlag 2011

On the Jacobson Element and Generators of the Lie Algebra grt in Nonzero Characteristic

Maria Podkopaeva
Université de Genève, Section de Mathématiques, 2-4 Rue du Lièvre -- CP 64, 1211 Genève 4, Switzerland

We state a conjecture (due to M. Duflo) analogous to the Kashiwara-Vergne conjecture in the case of a characteristic p>2, where the role of the Campbell-Hausdorff series is played by the Jacobson element. We prove a simpler version of this conjecture using Vergne's explicit rational solution of the Kashiwara-Vergne problem. Our result is related to the structure of the Grothendieck-Teichmüller Lie algebra grt in characteristic p: we conjecture existence of a generator of grt in degree p-1, and we provide this generator for p = 3 and p = 5.

Keywords: Kashiwara-Vergne conjecture, Grothendieck-Teichmueller Lie algebra, Jacobson element.

MSC: 22E60, 17B01

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