English

Pre- and Post-Lie Algebras: The Algebro-Geometric View

Algebraic Geometry 2017-04-21 v1 Rings and Algebras

Abstract

We relate composition and substitution in pre- and post-Lie algebras to algebraic geometry. The Connes-Kreimer Hopf algebras, and MKW Hopf algebras are then coordinate rings of the infinite-dimensional affine varieties consisting of series of trees, resp.\ Lie series of ordered trees. Furthermore we describe the Hopf algebras which are coordinate rings of the automorphism groups of these varieties, which govern the substitution law in pre- and post-Lie algebras.

Keywords

Cite

@article{arxiv.1704.06171,
  title  = {Pre- and Post-Lie Algebras: The Algebro-Geometric View},
  author = {Gunnar Fløystad and Hans Munthe-Kaas},
  journal= {arXiv preprint arXiv:1704.06171},
  year   = {2017}
}