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Journal of Lie Theory 18 (2008), No. 3, 617--626
Copyright Heldermann Verlag 2008

Solution Non Universelle pour le Problème KV-78

Luc Albert
Lycée Massena, 2 Avenue Félix Faure, 06050 Nice 1, France

Pascale Harinck
École Polytechnique, CMLS et CNRS, 91128 Palaiseau, France

Charles Torossian
Université Paris 7, IMJ et CNRS, Site Chevaleret, 2 place Jussieu, 75205 Paris 13, France


In 1978, M. Kashiwara and M. Vergne conjectured some property on the Campbell-Hausdorff series in such way that a trace formula is satisfied. They proposed an explicit solution in the case of solvable Lie algebras. In this note, we prove that this {\it solvable solution} is not universal. Our method is based on computer calculation. Furthermore our programs prove up to degree 16, Drinfeld's Lie algebra ${\frak grt}_1$ coincides with the Lie algebra $\widehat{{\frak kv}_2}$ defined in A. Alekseev and C. Torossian: The Kashiwara-Vergne conjecture and Drinfeld's associators, arXiv: 0802.4300.

Keywords: Free Lie algebra, Campbell-Hausdorff formula.

MSC: 17B01, 22E60, 68-04

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