Work

Novikov algebras and multi-indices in regularity structures

Year: 2026

Type: article

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.

Source: Annales Henri Lebesgue

DOI: 10.5802/ahl.275

Authors: Yvain Bruned, Vladimir Dotsenko

Institutions: Centre National de la Recherche Scientifique, Institut Élie Cartan de Lorraine, Université de Lorraine, Institut de Recherche Mathématique Avancée, Université de Strasbourg

Language: English

Topic: Advanced Topics in Algebra

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Agence Nationale de la Recherche, Institut Universitaire de France

Awards: Higher Algebra, Geometry, and Topology, G5296751580