Geodesic
The Baker-Campbell-Hausdorff Formula in the Free Metabelian Lie Algebra
Journal of Lie theory, Tome 17 (2007) no. 3, pp. 525-538.

Voir la notice de l'article provenant de la source Heldermann Verlag

The classical Baker-Campbell-Hausdorff formula gives a recursive way to compute the Hausdorff series $H=\ln(e^Xe^Y)$ for non-commuting $X,Y$. Formally $H$ lives in the graded completion of the free Lie algebra $L$ generated by $X,Y$. We present a closed explicit formula for $H=\ln(e^Xe^Y)$ in a linear basis of the graded completion of the free metabelian Lie algebra $L/[[L,L],[L,L]]$.
Classification : 17B01
Mots-clés : Lie algebra, metabelian Lie algebra, Hausdorff series, Baker-Campbell-Hausdorff formula, metabelian BCH formula, Zassenhaus formula, Kashiwara-Vergne conjecture 
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     author = {V. Kurlin },
     title = {The {Baker-Campbell-Hausdorff} {Formula} in the {Free} {Metabelian} {Lie} {Algebra}},
     journal = {Journal of Lie theory},
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     publisher = {mathdoc},
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     year = {2007},
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V. Kurlin . The Baker-Campbell-Hausdorff Formula in the Free Metabelian Lie Algebra. Journal of Lie theory, Tome 17 (2007) no. 3, pp. 525-538. http://geodesic.mathdoc.fr/item/JLT_2007_17_3_JLT_2007_17_3_a4/