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# The Baker-Campbell-Hausdorff formula in the free metabelian lie algebra.

Kurlin, V. (2007) 'The Baker-Campbell-Hausdorff formula in the free metabelian lie algebra.', Journal of lie theory., 17 (3). pp. 525-538.

## Abstract

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 $L/[[L,L],[L,L]]$.

Item Type: Article Lie algebra, metabelian Lie algebra, Hausdorff series, Baker-Campbell-Hausdorff formula, metabelian BCH formula, Zassenhaus formula, Kashiwara-Vergne conjecture. Full text not available from this repository. http://www.heldermann.de/JLT/JLT17/JLT173/jlt17027.htm 21 Sep 2007 23 Aug 2011 14:51

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