Groupes de renormalisation pour deux alg\`ebres de Hopf en produit semi-direct

TL;DR

This paper extends the concept of renormalization groups and Beta functions to a setting involving two interacting graded Hopf algebras, generalizing previous frameworks by replacing the graduation operator with biderivations derived from infinitesimal characters.

Contribution

It introduces a novel approach to renormalization in Hopf algebra theory by defining analogues of the renormalization group and Beta function using biderivations from infinitesimal characters.

Findings

Defined renormalization group analogues for Hopf algebras

Generalized Beta function concept in the Hopf algebra context

Applicable to interacting graded Hopf algebras

Abstract

We consider two interacting connected graded Hopf algebras, the former being a comodule-coalgebra on the latter. We show how to define analogues of Connes-Kreimer's renormalization group and Beta function, when the graduation operator is replaced by any biderivation coming from an infinitesimal character of the second Hopf algebra.