Extension of the product of a post-Lie algebra and application to the SISO feedback transformation group

Loïc Foissy (1)

1 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville

We describe the both post-and pre-Lie algebra 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 g SISO and its dual.

Mots clés: Post-Lie algebras; feedback transformation group; solvable Lie algebras

Domaines: Anneaux et algèbres [math.RA]

Loïc Foissy. Extension of the product of a post-Lie algebra and application to the SISO feedback transformation group. Computation and combinatorics in dynamics, stochastics and control, Aug 2016, Rosendal, Norway. ⟨10.1007/978-3-030-01593-0_13⟩. ⟨hal-01526056⟩