The Baker-Campbell-Hausdorff Formula in the Free Metabelian Lie Algebra

Kurlin, V

The Baker-Campbell-Hausdorff Formula in the Free Metabelian Lie Algebra

Kurlin, V

Authors

V Kurlin

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

Citation

Kurlin, V. (2007). The Baker-Campbell-Hausdorff Formula in the Free Metabelian Lie Algebra. Journal of Lie theory, 17(3), 525-538

Journal Article Type	Article
Publication Date	Aug 1, 2007
Deposit Date	Sep 21, 2007
Journal	Journal of Lie Theory
Print ISSN	0949-5932
Publisher	Heldermann Verlag
Peer Reviewed	Peer Reviewed
Volume	17
Issue	3
Pages	525-538
Keywords	Lie algebra, metabelian Lie algebra, Hausdorff series, Baker-Campbell-Hausdorff formula, metabelian BCH formula, Zassenhaus formula, Kashiwara-Vergne conjecture.
Publisher URL	http://www.heldermann.de/JLT/JLT17/JLT173/jlt17027.htm