Novikov algebras and multi-indices in regularity structures

Yvain Bruned; Vladimir Dotsenko

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arXiv · 2311.09091

Novikov algebras and multi-indices in regularity structures

Yvain Bruned·Vladimir Dotsenko

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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.

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Yvain Bruned, Vladimir Dotsenko. 2023-11-15. Novikov algebras and multi-indices in regularity structures. https://arxiv.org/abs/2311.09091

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