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math.RA2017★ 1 cited
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…
math.CO2017★ 2 cited
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…