Post-Lie deformations of pre-Lie algebras and their applications in Regularity Structures
Abstract
In this paper, we study post-Lie deformations of a pre-Lie algebra, namely deforming a pre-Lie algebra into a post-Lie algebra. We construct the differential graded Lie algebra that governs post-Lie deformations of a pre-Lie algebra. We also develop the post-Lie cohomology theory for a pre-Lie algebra, by which we classify infinitesimal post-Lie deformations of a pre-Lie algebra using the second cohomology group. The rigidity of such kind of deformations is also characterized using the second cohomology group. Finally, we apply this deformation theory to Regularity Structures. We prove that the post-Lie algebraic structure on the decorated trees which appears spontaneously in Regularity Structures is a post-Lie deformation of a pre-Lie algebra.
Keywords
Cite
@article{arxiv.2505.00456,
title = {Post-Lie deformations of pre-Lie algebras and their applications in Regularity Structures},
author = {Yvain Bruned and Yunhe Sheng and Rong Tang},
journal= {arXiv preprint arXiv:2505.00456},
year = {2025}
}
Comments
16 pages