A Magnus- and Fer-type formula in dendriform algebras

Details A Magnus- and Fer-type formula in dendriform algebras A Magnus- and Fer-type formula in dendriform algebras

2007-07-04

arxiv.org/abs/0707.0607v3

Foundations of Computational Mathematics, Volume 9, Issue3 (2009), 295.

Mathematics

Combinatorics

13 pages, LaTeX. Terminology issues fixed. Page setup problems fixed on pdf file. Final version as to appear in Foundations of

Scientific paper

10.1007/s10208-008-9023-3

We provide a refined approach to the classical Magnus and Fer expansion, unveiling a new structure by using the language of dendriform and pre-Lie algebras. The recursive formula for the logarithm of the solutions of the equations X=1+ta a in A[[t]] is provided, where (A,<,>) is a dendriform algebra. Then, we present the solutions to these equations as an infinite product expansion of exponentials. Both formulae involve the pre-Lie product naturally associated with the dendriform structure. Several applications are presented.

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