Solution non universelle pour le problème KV-78

Luc Albert (1) , Pascale Harinck (2) , Charles Torossian (3)

1 Lycée Massena
2 CMLS - Centre de Mathématiques Laurent Schwartz
3 IMJ - Institut de Mathématiques de Jussieu

In 78' M. Kashiwara and Vergne conjectured some property on the Campbell-Hausdorff series in such way a trace formula is satisfied. They proposed an explicit solution in the case of solvable Lie algebras. In this note we prove that this "solvable solution" is not universal. Our method is based on computer calculation. Furthermore our programs prove up to degree 16, Drinfeld's Lie algebra $\mathfrak{grt}_1$ coincides with the Lie algebra $\widehat{kv_2}$ defined in \cite{AT}.

Domaines: Algèbres quantiques [math.QA]; Théorie des groupes [math.GR]

Luc Albert, Pascale Harinck, Charles Torossian. Solution non universelle pour le problème KV-78. 2008. ⟨hal-00256194v3⟩