A Magnus- and Fer-type formula in dendriform algebras

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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<X and Y=1-tY> 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.
13 pages, LaTeX. Terminology issues fixed. Page setup problems fixed on pdf file. Final version as to appear in Foundations of Computational Mathematics

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Combinatorics, Mathematical Physics, Classical Analysis and ODEs, Rings and Algebras, 05E99; 16W99

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http://salesiana.dossiersoluciones.com/handle/123456789/226348

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0707.0607
 http://arxiv.org/abs/0707.0607
 Foundations of Computational Mathematics, Volume 9, Issue3 (2009), 295.
 doi:10.1007/s10208-008-9023-3

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arXiv