On the Jacobson element and generators of the Lie algebra $\mathfrak{grt}$ in nonzero characteristic

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dc.creatorPodkopaeva, Maria
dc.date2008-12-03
dc.date2008-12-04
dc.date.accessioned2026-07-07T12:09:04Z
dc.date.available2026-07-07T12:09:04Z
dc.descriptionWe 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 $\mathfrak{grt}$ in characteristic $p$: we conjecture existence of a generator of $\mathfrak{grt}$ in degree $p-1$, and we provide this generator for $p=3$ and $p=5$.
dc.descriptiontypos corrected
dc.identifierhttps://arxiv.org/abs/0812.0772
dc.identifierhttp://arxiv.org/abs/0812.0772
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/209501
dc.subjectQuantum Algebra
dc.subjectRepresentation Theory
dc.titleOn the Jacobson element and generators of the Lie algebra $\mathfrak{grt}$ in nonzero characteristic
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