What does this research mean for the field?

Multi-indices used in singular stochastic partial differential equations can be interpreted as free multi-Novikov algebras, which are a generalization of Novikov algebras with multiple binary operations. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To introduce multi-Novikov algebras and establish an algebraic foundation for the multi-indices utilized in the analysis of singular stochastic partial differential equations.

September 14, 2026Annales Henri LebesgueOpen Access

Novikov algebras and multi-indices in regularity structures

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Authors

YBYvain Bruned VDVladimir Dotsenko

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Overview

Theoretical analysis demonstrates that multi-indices in singular stochastic partial differential equations form free multi-Novikov algebras, highlighting parallels with decorated rooted trees.

Key Points

To introduce multi-Novikov algebras and establish an algebraic foundation for the multi-indices utilized in the analysis of singular stochastic partial differential equations.
Formulated multi-Novikov algebras by generalizing standard Novikov algebra axioms across a family of binary operations indexed by an arbitrary set.
Analyzed the formal algebraic properties of multi-indices within regularity structures by constructing free multi-Novikov algebra isomorphisms.
Proved that multi-indices arising in singular stochastic partial differential equations correspond to free multi-Novikov algebras.
Identified an algebraic duality showing this formulation parallels the relationship between decorated rooted trees and free multi-pre-Lie algebras in regularity structures.

Cite This Study

Bruned et al. (2026) studied this question.

synapsesocial.com/papers/6aa7b23b0926e14a848b089e https://doi.org/10.5802/ahl.275

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September 14, 2026Annales Henri LebesgueOpen Access

Novikov algebras and multi-indices in regularity structures

View Full Paper

Ask AI

Bookmark

Authors

YBYvain Bruned VDVladimir Dotsenko

Discussion

Member takes

Overview

Theoretical analysis demonstrates that multi-indices in singular stochastic partial differential equations form free multi-Novikov algebras, highlighting parallels with decorated rooted trees.

Key Points

To introduce multi-Novikov algebras and establish an algebraic foundation for the multi-indices utilized in the analysis of singular stochastic partial differential equations.
Formulated multi-Novikov algebras by generalizing standard Novikov algebra axioms across a family of binary operations indexed by an arbitrary set.
Analyzed the formal algebraic properties of multi-indices within regularity structures by constructing free multi-Novikov algebra isomorphisms.
Proved that multi-indices arising in singular stochastic partial differential equations correspond to free multi-Novikov algebras.
Identified an algebraic duality showing this formulation parallels the relationship between decorated rooted trees and free multi-pre-Lie algebras in regularity structures.

Cite This Study

Bruned et al. (2026) studied this question.

synapsesocial.com/papers/6aa7b23b0926e14a848b089e https://doi.org/10.5802/ahl.275

View Full Paper

Ask AI

Bookmark