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

2017/05/23 by Loïc Foissy, Foissy, Loïc · 2 citations
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1705.08132

openalex publication_date 2017/05/23 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• Post-Hopf algebroids, post-Lie-Rinehart algebras and geometric numerical integration
• An infinitesimal deformation of the post-Lie and post-Hopf algebra correspondence

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