11 papers
Bialgebraic structures on boolean functions
Loïc Foissy
We study several bialgebraic structures on boolean functions, that is to say maps defined on the set of subsets of a finite set , taking the value on . Examples o…
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…
Operads and bialgebras of multi-indices, and Novikov algebras
Loïc Foissy
Noncommutative multi-indices are noncommutative monomials in a -indexed family of indeterminates. We define on them a -graded operadic structure, with the h…
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…
Cocycle weighted infinitesimal bialgebras and pre-Lie algebras on rooted trees
Loïc Foissy, Yunzhou Xie, Dawei Zhang +1
The concept of weighted infinitesimal bialgebras provides an algebraic framework for understanding the non-homogeneous associative Yang-Baxter equation. In this paper, we endow the…
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…