12 citations · 76 across the 61 of their papers we have counts for
6 papers · 2 filters
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…
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…
Construction of pre-and post-Lie algebras for stochastic PDEs
Loïc Foissy
We give and study a construction of pre-Lie algebra structures on rooted trees whose edges and vertices are decorated, with a grafting product acting, through a map , both on th…
Matrix symmetric and quasi-symmetric functions and noncommutative representation theory
Loïc Foissy, Claudia Malvenuto, Frédéric Patras
A fundamental result by L. Solomon in algebraic combinatorics and representation theory states that Mackey formulas for products of characters of a symmetric group, or equivalently…
Species of Rota-Baxter algebras by rooted trees, twisted bialgebras and Fock functors
Loic Foissy, Li Guo, Xiao-Song Peng +2
As a fundamental and ubiquitous combinatorial notion, species has attracted sustained interest, generalizing from set-theoretical combinatorial to algebraic combinatorial and beyon…
Cointeraction on noncrossing partitions and related polynomial invariants
Loïc Foissy
We study the structure of two cointeracting bialgebras on noncrossing partitions appearing in the theory of free probability. The first coproduct is given by separation of the bloc…