5 citations · 11 across the 7 of their papers we have counts for
8 papers
An operad is never free as a pre-Lie algebra
Emily Burgunder, Bérénice Delcroix-Oger, Dominique Manchon
An operad is naturally endowed with a pre-Lie structure. We prove that as a pre-Lie algebra an operad is not free. The proof holds on defining a non-vanishing linear operation in t…
Confluence laws and Hopf-Borel type theorem for operads
Emily Burgunder, Bérénice Delcroix-Oger
In 2008, Loday shed light on the existence of Hopf-Boreltheorems for operads. Using the vocabulary of category theory, Livernet,Mesablishvili and Wisbauer extended such theorems to…
Free algebraic structures on the permutohedra
E. Burgunder, P. -L. Curien, M. Ronco
Tridendriform algebras are a type of associative algebras, introduced independently by F. Chapoton and by J.-L. Loday and the third author, in order to describe operads related to…
Tridendriform structure on combinatorial Hopf algebras
Emily Burgunder, Maria Ronco
We extend the definition of tridendriform bialgebra by introducing a weight q. The subspace of primitive elements of a q-tridendriform bialgebra is equipped with an associative pro…
A symmetric version of Kontsevich graph complex and Leibniz homology
Emily Burgunder
Kontsevich has proven that the Lie homology of the Lie algebra of symplectic vector fields can be computed in terms of the homology of a graph complex. We prove that the Leibniz ho…
Partial magmatic bialgebras
Emily Burgunder, Ralf Holtkamp
A partial magmatic bialgebra, (T;S)-magmatic bialgebra where T \subset S are subsets of the set of positive integers, is a vector space endowed with an n-ary operation for each n i…