Geodesic
The Baker-Campbell-Hausdorff Formula in the Free Metabelian Lie Algebra
Vitaliy Kurlin1
1Department of Mathematics, University of Liverpool, Liverpool L69 7ZL, England
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

Vitaliy Kurlin  1

1 Department of Mathematics, University of Liverpool, Liverpool L69 7ZL, England 
Vitaliy 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/JOLT_2007_17_3_a4/
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     author = {Vitaliy Kurlin},
     title = {The {Baker-Campbell-Hausdorff} {Formula} in the {Free} {Metabelian} {Lie} {Algebra}},
     journal = {Journal of Lie Theory},
     pages = {525--538},
     year = {2007},
     volume = {17},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2007_17_3_a4/}
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