Let L = L(x 1 ,..., x m ) be a graded Lie algebra generated by {x 1 ,...,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(λ i x i ). We give an explicit construction that avoids any calculation in the Lie algebra.
['Frédéric Jean', 'Pierre-Vincent Koseleff']
Elementary Approximation of Exponentials of Lie Polynominals