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H 1 Free post-Lie algebras, the Hopf algebra of Lie group integrators and planar arborification

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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.
    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 #.

    Codes MSC :
    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

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 06/07/17
      Date de captation : 29/06/17
      Collection : Research talks ; Algebra ; Combinatorics ; Lie Theory and Generalizations ; Mathematical Physics
      Format : MP4
      Durée : 01:00:09
      Domaine : Mathematical Physics ; Algebra ; Lie Theory and Generalizations ; Combinatorics
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2017-06-29_Manchon.mp4

    Informations sur la rencontre

    Nom de la rencontre : Algebraic combinatorics, resurgence, moulds and applications / Combinatoire algébrique, résurgence, moules et applications
    Dates : 26/06/17 - 30/06/17
    Année de la rencontre : 2017
    URL Congrès : http://conferences.cirm-math.fr/1599.html

    Citation Data

    DOI : 10.24350/CIRM.V.19190803
    Cite this video as: (2017). Free post-Lie algebras, the Hopf algebra of Lie group integrators and planar arborification. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19190803
    URI : http://dx.doi.org/10.24350/CIRM.V.19190803

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