Extension of the Product of a Post-Lie Algebra and Application to the SISO Feedback Transformation Group

  • Loïc FoissyEmail author
Conference paper
Part of the Abel Symposia book series (ABEL, volume 13)


We describe both post- and pre-Lie algebra \(\mathfrak {g}_{SISO}\) associated to the affine SISO feedback transformation group. We show that it is a member of a family of post-Lie algebras associated to representations of a particular solvable Lie algebra. We first construct the extension of the magmatic product of a post-Lie algebra to its enveloping algebra, which allows to describe free post-Lie algebras and is widely used to obtain the enveloping of \(\mathfrak {g}_{SISO}\) and its dual.



The research leading these results was partially supported by the French National Research Agency under the reference ANR-12-BS01-0017.


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Authors and Affiliations

  1. 1.Fédération de Recherche Mathématique du Nord Pas de Calais FR 2956, Laboratoire de Mathématiques Pures et Appliquées Joseph LiouvilleUniversité du Littoral Côte d’Opale-Centre Universitaire de la Mi-VoixCalais CedexFrance

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