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arXiv · 0707.0607

A Magnus- and Fer-type formula in dendriform algebras

Kurusch Ebrahimi-Fard·Dominique Manchon
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Abstract

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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Kurusch Ebrahimi-Fard, Dominique Manchon. 2008-01-10. A Magnus- and Fer-type formula in dendriform algebras. https://doi.org/10.1007/s10208-008-9023-3

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