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

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

2006-06-14

arxiv.org/abs/math/0606330v4

Mathematics

Quantum Algebra

10 pages, the paper was completely reworked. The metabelian BCH formula is interpreted as a linear part of a deeper formula fo

Scientific paper

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]].

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