Multi angle Free post-Lie algebras, the Hopf algebra of Lie group integrators and planar arborification
Auteurs : Manchon, Dominique (Auteur de la Conférence)
CIRM (Editeur )
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Résumé : The Hopf algebra of Lie group integrators has been introduced by H. Munthe-Kaas and W. Wright as a tool to handle Runge-Kutta numerical methods on homogeneous spaces. It is spanned by planar rooted forests, possibly decorated. We will describe a canonical surjective Hopf algebra morphism onto the shuffle Hopf algebra which deserves to be called planar arborification. The space of primitive elements is a free post-Lie algebra, which in turn will permit us to describe the corresponding co-arborification process.Codes MSC :
Joint work with Charles Curry (NTNU Trondheim), Kurusch Ebrahimi-Fard (NTNU) and Hans Z. Munthe-Kaas (Univ. Bergen).
The two triangles appearing at 24'04" and 25'19'' respectively should be understood as a #.
05C05 - Trees
17D25 - Lie-admissible algebras
65L06 - Multistep, Runge-Kutta and extrapolation methods
81T15 - Perturbative methods of renormalization (quantum theory)
16T05 - Hopf algebras and their applications