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Peer-reviewedCC BYAnnales Henri Lebesgue

Novikov algebras and multi-indices in regularity structures

  • Yvain Bruned1,2
  • Vladimir Dotsenko3,4
4 affiliations
  1. 1Université de Lorraine, CNRS, IECL, 54000 Nancy (France)
  2. 2Institut Élie Cartan de Lorraine
  3. 3Université de Strasbourg, CNRS, IRMA, 67000 Strasbourg (France)
  4. 4Institut de Recherche Mathématique Avancée
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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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Cite

BibTeXRIS
BibTeX
@article{bruned2026novikov,
  title = {{Novikov algebras and multi-indices in regularity structures}},
  author = {Yvain Bruned and Vladimir Dotsenko},
  journal = {Annales Henri Lebesgue},
  year = {2026},
  month = sep,
  doi = {10.5802/ahl.275},
  url = {https://doi.org/10.5802/ahl.275},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Novikov algebras and multi-indices in regularity structures
AU  - Yvain Bruned
AU  - Vladimir Dotsenko
PY  - 2026
DA  - 2026/09/11
JO  - Annales Henri Lebesgue
DO  - 10.5802/ahl.275
UR  - https://doi.org/10.5802/ahl.275
AB  - 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.
SN  - 2644-9463
ER  -