Journal of Lie Theory

no. 1
On the Jacobson Element and Generators of the Lie Algebra grt in Nonzero Characteristic
Journal of Lie Theory, Volume 21 (2011) no. 1, pp. 71-78
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.
DOI: 10.5802/jolt.623
Classification: 22E60, 17B01
Keywords: Kashiwara-Vergne conjecture, Grothendieck-Teichmueller Lie algebra, Jacobson element 
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     author = {M. 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},
     doi = {10.5802/jolt.623},
     zbl = {1208.22010},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.623/}
}
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M. Podkopaeva. On the Jacobson Element and Generators of the Lie Algebra grt in Nonzero Characteristic. Journal of Lie Theory, Volume 21 (2011) no. 1, pp. 71-78. doi: 10.5802/jolt.623

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