The Hopf algebra of Fliess operators and its dual pre-Lie algebra - Archive ouverte HAL Access content directly
Journal Articles Communications in Algebra Year : 2015

The Hopf algebra of Fliess operators and its dual pre-Lie algebra

Abstract

We study the Hopf algebra H of Fliess operators coming from Control Theory in the one-dimensional case. We prove that it admits a graded, finte-dimensional, connected gradation. Dually, the vector space IR is both a pre-Lie algebra for the pre-Lie product dual of the coproduct of H, and an associative, commutative algebra for the shuffle product. These two structures admit a compatibility which makes IR a Com-pre-Lie algebra. We give a presentation of this object as a Com-pre-Lie algebra and as a pre-Lie algebra.
Fichier principal
Vignette du fichier
control.pdf (304.62 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-00808513 , version 1 (05-04-2013)
hal-00808513 , version 2 (04-06-2013)
hal-00808513 , version 3 (21-02-2014)

Identifiers

Cite

Loïc Foissy. The Hopf algebra of Fliess operators and its dual pre-Lie algebra. Communications in Algebra, 2015. ⟨hal-00808513v3⟩
255 View
326 Download

Altmetric

Share

Gmail Facebook X LinkedIn More