Volume 9 (2026)
Bruned, Yvain ; Dotsenko, Vladimir
Novikov algebras and multi-indices in regularity structures
Annales Henri Lebesgue, Volume 9 (2026), pp. 791-814

Metadata

DOI10.5802/ahl.275
Keywords Multi-indices ,  Novikov algebras ,  Regularity Structures ,  Singular SPDEs

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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