The Baker-Campbell-Hausdorff formula in the free metabelian Lie algebra


Kurlin, Vitaliy ORCID: 0000-0001-5328-5351 (2007) The Baker-Campbell-Hausdorff formula in the free metabelian Lie algebra. JOURNAL OF LIE THEORY, 17 (3). pp. 525-538.

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Abstract

The classical Baker-Campbell-Hausdorff formula gives a recursive way to compute the Hausdorff series H=ln(e^X e^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^X e^Y) in a linear basis of the graded completion of the free metabelian Lie algebra L/[[L,L],[L,L]].

Item Type: Article
Additional Information: 10 pages, the paper was completely reworked. The metabelian BCH formula is interpreted as a linear part of a deeper formula for ln(e^X e^Y)
Uncontrolled Keywords: Lie algebra, metabelian Lie algebra, Hausdorff series, Baker-Campbell-Hausdorff formula, metabelian BCH formula, Zassenhaus formula, Kashiwara-Vergne conjecture.
Depositing User: Symplectic Admin
Date Deposited: 14 Dec 2016 15:24
Last Modified: 19 Jan 2023 07:24
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URI: https://livrepository.liverpool.ac.uk/id/eprint/3004870
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