Journal of Lie Theory

no. 3
The Baker-Campbell-Hausdorff Formula in the Free Metabelian Lie Algebra
Journal of Lie Theory, Volume 17 (2007) no. 3, pp. 525-538
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 $L/[[L,L],[L,L]]$.
DOI: 10.5802/jolt.459
Classification: 17B01
Keywords: Lie algebra, metabelian Lie algebra, Hausdorff series, Baker-Campbell-Hausdorff formula, metabelian BCH formula, Zassenhaus formula, Kashiwara-Vergne conjecture 
@article{JOLT_2007_17_3_a4,
     author = {V. Kurlin},
     title = {The {Baker-Campbell-Hausdorff} {Formula} in the {Free} {Metabelian} {Lie} {Algebra}},
     journal = {Journal of Lie Theory},
     pages = {525--538},
     year = {2007},
     volume = {17},
     number = {3},
     doi = {10.5802/jolt.459},
     zbl = {1135.17001},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.459/}
}
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V. Kurlin. The Baker-Campbell-Hausdorff Formula in the Free Metabelian Lie Algebra. Journal of Lie Theory, Volume 17 (2007) no. 3, pp. 525-538. doi: 10.5802/jolt.459

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