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

Kurlin, V

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.
• Public URL: https://durham-repository.worktribe.com/output/1567424
• Publisher URL: http://www.heldermann.de/JLT/JLT17/JLT173/jlt17027.htm