Elementary Approximation of Exponentials of Lie Polynominals

Let L=l(x1,..., xm) be a graded Lie algebra generated by x1,..., x m . In this paper, we show that for any element P in L and any order k, exp(P) may be approximated at the order k by a finite product of elementary factors exp(λi,xi,). We give an explicit construction that avoids any calculation in the Lie algebra.

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