Fà a Di Bruno Hopf Algebras

Combinatorial Hopf algebras from PROs

We introduce a general construction that takes as input a so-called stiff PRO and that outputs a Hopf algebra. Stiff PROs are particular PROs that can be described by generators and relations with precise conditions. Our construction generalizes the classical construction from operads to Hopf algebras of van der Laan. We study some of its properties and review some examples of application. We g...

On the Coderivations of Some Hopf Algebras

NOTES ON REGULAR MULTIPLIER HOPF ALGEBRAS

In this paper, we associate canonically a precyclic mod- ule to a regular multiplier Hopf algebra endowed with a group-like projection and a modular pair in involution satisfying certain con- dition

A one-parameter deformation of the Farahat-Higman algebra

We show, by introducing an appropriate basis, that a one-parameter family of Hopf algebras introduced by Foissy [Adv. Math. 218 (2008) 136-162] interpolates beetween the Faà di Bruno algebra and the Farahat-Higman algebra. Its structure constants in this basis are deformation of the top connection coefficients, for which we obtain analogues of Macdonald’s formulas.

Hopf Algebras of Formal Diffeomorphisms and Numerical Integration on Manifolds

B-series originated from the work of John Butcher in the 1960s as a tool to analyze numerical integration of differential equations, in particular Runge–Kutta methods. Connections to renormalization have been established in recent years. The algebraic structure of classical Runge–Kutta methods is described by the Connes–Kreimer Hopf algebra. Lie–Butcher theory is a generalization of B-series ai...