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Elementary approximation of exponentials of Lie polynomials. (English) Zbl 1039.17500

Mora, Teo (ed.) et al., Applied algebra, algebraic algorithms and error-correcting codes. 12th international symposium, AAECC-12, Toulouse, France, June 23–27, 1997. Proceedings. Berlin: Springer (ISBN 3-540-63163-1). Lect. Notes Comput. Sci. 1255, 174-188 (1997).
Summary: Let \({\mathcal L} = L(x_1,\dots,x_m)\) be a graded Lie algebra generated by \(\{x_1,\dots,x_m\}\). In this paper, we show that for any element \(P\) in \({\mathcal L}\) and any order \(k\), \(\exp(P)\) may be approximated at the order \(k\) by a finite product of elementary factors \(\exp(\lambda_i x_i)\). We give an explicit construction that avoids any calculation in the Lie algebra.
For the entire collection see [Zbl 1001.00072].

MSC:

17-08 Computational methods for problems pertaining to nonassociative rings and algebras
17B01 Identities, free Lie (super)algebras
17B70 Graded Lie (super)algebras
41A99 Approximations and expansions
65D99 Numerical approximation and computational geometry (primarily algorithms)
93B25 Algebraic methods
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