The pre Lie relation rooted trees and the Magnus expansion

Description

The pre-Lie relation, rooted trees and the Magnus expansion Kurusch Ebrahimi-Fard? Universite de Haute Alsace Mulhouse, France Conference Algebre combinatoire et Arbres Lyon, 29 May, 2008 ?joint work with D. Manchon

• magnus expansion


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• conference algebre combinatoire


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• kurusch ebrahimi-fard?

Sujets

• Magnus expansion

Informations

• Publié par: profil-urra-2012
• Nombre de lectures: 9
• Langue: English

Extrait

The pre-Lie relation, rooted trees and the Magnus expansion

Kurusch Ebrahimi-Fard

Universite´deHauteAlsace Mulhouse, France

∗

Confe´renceAlge`brecombinatoireetArbres Lyon, 29 May, 2008

∗ joint work with D. Manchon

Motivation

1) initial value problem I ˙ f ( t ) = a ( t ) f ( t ) 

f (0) = 1

I ( f )( t ) := Z 0 t f ( s ) ds f = 1 + I ( af ) f = 1 + X I ( ( a ))   I  a  {   I ( aI }  )  n> 0 n - times

a ≺ f := aI ( f )

f = 1 + I  a + X 1 a ≺ (   {  ≺ ( a ≺ } a )    )  n> n - times ˙ ˙ f = a + a ≺ f

( a ≺ b ) ≺ c = aI ( b ) I ( c ) = aI  I ( b ) c + b I ( c )  = a ≺  b ≻ c + b ≺ c 