A Magnus- and Fer-type formula in dendriform algebras

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dc.creatorEbrahimi-Fard, Kurusch
dc.creatorManchon, Dominique
dc.date2007-07-04
dc.date2008-01-10
dc.date.accessioned2026-07-07T13:02:02Z
dc.date.available2026-07-07T13:02:02Z
dc.descriptionWe 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.
dc.description13 pages, LaTeX. Terminology issues fixed. Page setup problems fixed on pdf file. Final version as to appear in Foundations of Computational Mathematics
dc.identifierhttps://arxiv.org/abs/0707.0607
dc.identifierhttp://arxiv.org/abs/0707.0607
dc.identifierFoundations of Computational Mathematics, Volume 9, Issue3 (2009), 295.
dc.identifierdoi:10.1007/s10208-008-9023-3
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/226348
dc.subjectCombinatorics
dc.subjectMathematical Physics
dc.subjectClassical Analysis and ODEs
dc.subjectRings and Algebras
dc.subject05E99; 16W99
dc.titleA Magnus- and Fer-type formula in dendriform algebras
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