Feuilleter
no. 2
Geometric embedding for regularity structures
[Plongement géométrique pour les structures de régularité]
Yvain Bruned1 ; Foivos Katsetsiadis2
1Universite de Lorraine, CNRS, IECL, 54000 Nancy, France
2ITI-CERTH, Thermi-Thessaloniki, Greece
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 35 (2026) no. 2, pp. 409-436

In this paper, we show how one can view certain models in regularity structures as some form of geometric rough paths. This is performed by identifying the deformed Butcher–Connes–Kreimer Hopf algebra with a quotient of the shuffle Hopf algebra which is the structure underlying the definition of a geometric rough path. This provides an extension of the isomorphism between the Butcher–Connes–Kreimer Hopf algebra and the shuffle Hopf algebra. This new algebraic result relies strongly on the deformation formalism and the post-Lie structures introduced recently in the context of regularity structures.

Dans cet article, on montre comment l’on peut voir certains modèles dans les structures de régularité sous la forme de chemins rugueux géométriques. On réalise cette construction en identifiant l’algèbre de Hopf de Butcher–Connes–Kreimer déformée avec le quotient d’une algèbre de shuffle qui est une structure présente dans la définition d’un chemin rugueux géométrique. Cela procure une extension de l’isomorphisme entre l’algèbre de Hopf de Butcher–Connes–Kreimer et celle de l’algèbre de shuffle. Ce résultat algébrique nouveau repose fortement sur le formalisme de déformation et la structure post-Lie introduite récemment dans le contexte des structures de régularité.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/afst.1851
Classification : 60L70, 60H15
Keywords: Hopf algebras, geometric rough paths, regularity structures, singular SPDEs, shuffle algebra
Mots-clés : Algèbres de Hopf, Algèbre de shuffle, Chemins rugueux géométriques, EDPS singulières, Structures de régularité

Yvain Bruned  1   ; Foivos Katsetsiadis  2

1 Universite de Lorraine, CNRS, IECL, 54000 Nancy, France
2 ITI-CERTH, Thermi-Thessaloniki, Greece
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
Yvain Bruned; Foivos Katsetsiadis. Geometric embedding for regularity structures. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 35 (2026) no. 2, pp. 409-436. doi: 10.5802/afst.1851
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