An operad is never free as a pre-Lie algebra
Rings and Algebras
2017-02-08 v1
Abstract
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 the pre-Lie algebra which is zero in any operad.
Keywords
Cite
@article{arxiv.1702.01949,
title = {An operad is never free as a pre-Lie algebra},
author = {Emily Burgunder and Bérénice Delcroix-Oger and Dominique Manchon},
journal= {arXiv preprint arXiv:1702.01949},
year = {2017}
}