English

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}
}