133 citations · 1.4k across the 77 of their papers we have counts for
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The symmetric operation in a free pre-Lie algebra is magmatic
Nantel Bergeron, Jean-Louis Loday
A pre-Lie product is a binary operation whose associator is symmetric in the last two variables. As a consequence its antisymmetrization is a Lie bracket. In this paper we study th…
Non-commutative Combinatorial Inverse Systems
J. -C. Aval, N. Bergeron, H. Li
We introduce the notion of a combinatorial inverse system in non-commutative variables. We present two important examples, some conjectures and results. These conjectures and resul…
The non-symmetric operad pre-Lie is free
Nantel Bergeron, Muriel Livernet
We prove that the pre-Lie operad is a free non-symmetric operad.
A combinatorial basis for the free Lie algebra of the labelled rooted trees
Nantel Bergeron, Muriel Livernet
The pre-Lie operad can be realized as a space T of labelled rooted trees. A result of F. Chapoton shows that the pre-Lie operad is a free twisted Lie algebra. That is, the S-module…
Algebraic Structures on Grothendieck Groups of a Tower of Algebras
Nantel Bergeron, Huilan Li
The Grothendieck group of the tower of symmetric group algebras has a self-dual graded Hopf algebra structure. Inspired by this, we introduce by way of axioms, a general notion of…