
Journal of Lie Theory 17 (2007), No. 3, 525538 Copyright Heldermann Verlag 2007 The BakerCampbellHausdorff Formula in the Free Metabelian Lie Algebra Vitaliy Kurlin Department of Mathematics, University of Liverpool, Liverpool L69 7ZL, England kurlin@liv.ac.uk [Abstractpdf] The classical BakerCampbellHausdorff formula gives a recursive way to compute the Hausdorff series $H=\ln(e^Xe^Y)$ for noncommuting $X,Y$. 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 $L/[[L,L],[L,L]]$. Keywords: Lie algebra, metabelian Lie algebra, Hausdorff series, BakerCampbellHausdorff formula, metabelian BCH formula, Zassenhaus formula, KashiwaraVergne conjecture. MSC: 17B01 [ Fulltextpdf (190 KB)] for subscribers only. 