Post-Lie algebras in Regularity Structures
Probability
2023-07-06 v5 Analysis of PDEs
Rings and Algebras
Abstract
In this work, we construct the deformed Butcher-Connes-Kreimer Hopf algebra coming from the theory of Regularity Structures as the universal envelope of a post-Lie algebra. We show that this can be done using either of the two combinatorial structures that have been proposed in the context of singular SPDEs: decorated trees and multi-indices. Our construction is inspired from multi-indices where the Hopf algebra was obtained as the universal envelope of a Lie algebra and it has been proved that one can find a basis that is symmetric with respect to certain elements. We show that this Lie algebra comes from an underlying post-Lie structure.
Keywords
Cite
@article{arxiv.2208.00514,
title = {Post-Lie algebras in Regularity Structures},
author = {Yvain Bruned and Foivos Katsetsiadis},
journal= {arXiv preprint arXiv:2208.00514},
year = {2023}
}