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Article Dans Une Revue Foundations of Computational Mathematics Année : 2009

A Magnus- and Fer-type formula in dendriform algebras

Résumé

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.

Dates et versions

hal-00483482 , version 1 (14-05-2010)

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Citer

Kurusch Ebrahimi-Fard, Dominique Manchon. A Magnus- and Fer-type formula in dendriform algebras. Foundations of Computational Mathematics, 2009, 9 (3), pp.295-316. ⟨10.1007/s10208-008-9023-3⟩. ⟨hal-00483482⟩
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