- Published 2008

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. Let lie2 be a free Lie algebra over a field K of characteristic zero with generators x and y. It is a graded Lie algebra lie2 = ∏ ∞ k=1 lie k 2 , where lie k 2 is spanned by the Lie words consisting of k letters. We denote by z = logee be the Campbell–Hausdorff series:

@inproceedings{Podkopaeva2008OnTJ,
title={On the Jacobson element and generators of the Lie algebra grt in nonzero characteristic},
author={Maria Podkopaeva},
year={2008}
}