12 citations · 76 across the 61 of their papers we have counts for
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Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach
Loic Foissy, Xiao-Song Peng, Yunzhou Xie +1
In this paper, we first endow the space of decorated planar rooted forests with a coproduct that equips it with the structure of a bialgebra and further a Moerdijk Hopf algebra. We…
Primitive elements of a connected free bialgebra
Loïc Foissy
We prove that the Lie algebra of primitive elements of a graded and connected bialgebra, free as an associative algebra, over a eld of characteristic zero, is a free Lie algebra. T…
Tensor products and the Milnor-Moore theorem in the locality setup
Pierre J. Clavier, Loic Foissy, Diego A. López +1
The present exploratory paper deals with tensor products in the locality framework {developed in previous work}, a natural setting for an algebraic formulation of the locality prin…
Bialgebras overs another bialgebras and quasishuffle double bialgebras
Loïc Foissy
Quasishuffle Hopf algebras, usually defined on a commutative monoid, can be more generally defined on any associative algebra V. If V is a commutative and cocommutative bialgebra,…
Bialgebras in cointeraction, the antipode and the eulerian idempotent
Loïc Foissy
We give here a review of results about double bialgebras, that is to say bialgebras with two coproducts, the first one being a comodule morphism for the coaction induced by the sec…
Reduced typed angularly decorated planar rooted trees and generalized tridendriform algebras
Loïc Foissy, Xiao-Song Peng
We introduce a generalization of tridendriform algebras, where each of the three products are replaced by a family of products indexed by a set . We study the needed structure o…
Typed angularly decorated planar rooted trees and generalized Rota-Baxter algebras
Loïc Foissy, Xiao-Song Peng
We introduce a generalization of parametrized Rota-Baxter algebras, which includes family and matching Rota-Baxter algebras. We study the structure needed on the set of paramet…
On extended associative semigroups
Loïc Foissy
We study extended associative semigroups (briefly, EAS), an algebraic structure used to define generalizations of the operad of associative algebras, and the subclass of commutativ…
Generalized prelie and permutative algebras
Loïc Foissy
We study generalizations of pre-Lie algebras, where the free objects are based on rooted trees which edges are typed, instead of usual rooted trees, and with generalized pre-Lie pr…
Generalized associative algebras
Loïc Foissy
We study diverse parametrized versions of the operad of associative algebra, where the parameter are taken in an associative semigroup (generalization of matching or family ass…
Families of algebraic structures
Loic Foissy, Dominique Manchon, Yuanyuan Zhang
We give a general account of family algebras over a finitely presented linear operad, this operad together with its presentation naturally defining an algebraic structure on the se…
Realizations of Hopf algebras of graphs by alphabets
Loïc Foissy
We here give polynomial realizations of various Hopf algebras or bialgebras on Feynman graphs, graphs, posets or quasi-posets, that it to say injections of these objects into polyn…
Twisted bialgebras, cofreeness and cointeraction
Loïc Foissy
We study twisted bialgebras and double twisted bialgebras, that is to say bialgebras in the category of linear species, or in the category of species in the category of coalgebras.…
Algebraic structures on typed decorated rooted trees
Loïc Foissy
Typed decorated trees are used by Bruned, Hairer and Zambotti to give a description of a renormalisation processon stochastic PDEs. We here study the algebraic structures on these…
Cofree Com-PreLie algebras
Loïc Foissy
A Com-PreLie bialgebra is a commutative bialgebra with an extra preLie product satisfying some compatibilities with the product and the coproduct. We here give examples of cofree C…
Extension of the product of a post-Lie algebra and application to the SISO feedback transformation group
Loïc Foissy
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 assoc…
Algebraic structures associated to operads
Loïc Foissy
We study different algebraic structures associated to an operad and their relations: to any operad is attached a bialgebra,the monoid of characters of this bialgebra,…
Chromatic polynomials and bialgebras of graphs
Loïc Foissy
The chromatic polynomial is characterized as the unique polynomial invariant of graphs, compatible with two interacting bialgebras structures: the first coproduct is given by parti…
Lie theory for quasi-shuffle bialgebras
Loïc Foissy, Frédéric Patras
Many features of classical Lie theory generalize to the broader context of algebras over Hopf operads. However, this idea remains largely to be developed systematically. Quasi-shuf…
Commutative and non-commutative bialgebras of quasi-posets and applications to Ehrhart polynomials
Loïc Foissy
To any poset or quasi-poset is attached a lattice polytope, whose Ehrhart polynomial we study from a Hopf-algebraic point of view. We use for this two interacting bialgebras on qua…
Mulitgraded Dyson-Schwinger systems
Loïc Foissy
We study systems of combinatorial Dyson-Schwinger equations with an arbitrary number of coupling constants. The considered Hopf algebra of Feynman graphs is -grad…
Examples of Com-PreLie Hopf algebras
Loïc Foissy
We gives examples of Com-PreLie bialgebras, that is to say bialgebras with a preLie product satisfying certain compatibilities. Three families are defined on shuffle algebras: one…
A prelie algebra associated to a linear endomorphism and related algebraic structures
Loïc Foissy
We attach to any linear endomorphism f of any vector space V a structure of prelie algebra on the shuffle algebra T(V); we describe its enveloping algebra, the dual Hopf algebra an…
The Hopf algebra of Fliess operators and its dual pre-Lie algebra
Loïc Foissy
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. Du…