
Journal of Lie Theory 18 (2008), No. 3, 617626 Copyright Heldermann Verlag 2008 Solution Non Universelle pour le Problème KV78 Luc Albert Lycée Massena, 2 Avenue Félix Faure, 06050 Nice 1, France luc@albert1.net Pascale Harinck École Polytechnique, CMLS et CNRS, 91128 Palaiseau, France harinck@math.polytechnique.fr Charles Torossian Université Paris 7, IMJ et CNRS, Site Chevaleret, 2 place Jussieu, 75205 Paris 13, France torossian@math.jussieu.fr [Abstractpdf] In 1978, M. Kashiwara and M. Vergne conjectured some property on the CampbellHausdorff 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 KashiwaraVergne conjecture and Drinfeld's associators, arXiv: 0802.4300. Keywords: Free Lie algebra, CampbellHausdorff formula. MSC: 17B01, 22E60, 6804 [ Fulltextpdf (192 KB)] for subscribers only. 