Geodesic
On the Jacobson Element and Generators of the Lie Algebra grt in Nonzero Characteristic
Maria Podkopaeva1
1Université de Genève, Section de Mathématiques, 2-4 Rue du Lièvre -- CP 64, 1211 Genève 4, Switzerland
Journal of Lie Theory, Tome 21 (2011) no. 1, pp. 71-78

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 22E60, 17B01
Mots-clés : Kashiwara-Vergne conjecture, Grothendieck-Teichmueller Lie algebra, Jacobson element

Maria Podkopaeva  1

1 Université de Genève, Section de Mathématiques, 2-4 Rue du Lièvre -- CP 64, 1211 Genève 4, Switzerland 
Maria Podkopaeva. On the Jacobson Element and Generators of the Lie Algebra grt in Nonzero Characteristic. Journal of Lie Theory, Tome 21 (2011) no. 1, pp. 71-78. http://geodesic.mathdoc.fr/item/JOLT_2011_21_1_a2/
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     author = {Maria Podkopaeva},
     title = {On the {Jacobson} {Element} and {Generators} of the {Lie} {Algebra} grt in {Nonzero} {Characteristic}},
     journal = {Journal of Lie Theory},
     pages = {71--78},
     year = {2011},
     volume = {21},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2011_21_1_a2/}
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