Journal of Lie Theory

no. 3
Solution Non Universelle pour le Problème KV-78
Journal of Lie Theory, Volume 18 (2008) no. 3, pp. 617-626
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.
DOI: 10.5802/jolt.515
Classification: 17B01, 22E60, 68-04
Keywords: Free Lie algebra, Campbell-Hausdorff formula 
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     author = {L. Albert and P. Harinck and C. Torossian},
     title = {Solution {Non} {Universelle} pour le {Probl\`eme} {KV-78}},
     journal = {Journal of Lie Theory},
     pages = {617--626},
     year = {2008},
     volume = {18},
     number = {3},
     doi = {10.5802/jolt.515},
     zbl = {1210.17006},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.515/}
}
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L. Albert; P. Harinck; C. Torossian. Solution Non Universelle pour le Problème KV-78. Journal of Lie Theory, Volume 18 (2008) no. 3, pp. 617-626. doi: 10.5802/jolt.515

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