Novikov algebras and multi-indices in regularity structures
Rings and Algebras
2026-05-26 v2 Analysis of PDEs
Probability
Abstract
In this work, we introduce multi-Novikov algebras, a generalisation of Novikov algebras with several binary operations indexed by a given set, and show that the multi-indices recently introduced in the context of singular stochastic partial differential equations can be interpreted as free multi-Novikov algebras. This is parallel to the fact that decorated rooted trees arising in the context of regularity structures are related to free multi-pre-Lie algebras.
Cite
@article{arxiv.2311.09091,
title = {Novikov algebras and multi-indices in regularity structures},
author = {Yvain Bruned and Vladimir Dotsenko},
journal= {arXiv preprint arXiv:2311.09091},
year = {2026}
}
Comments
To appear in Annales Henri Lebesgue