Novikov algebras and multi-indices in regularity structures
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916043581030400 |
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| author | Bruned, Yvain Dotsenko, Vladimir |
| author_facet | Bruned, Yvain Dotsenko, Vladimir |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_09091 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Novikov algebras and multi-indices in regularity structures Bruned, Yvain Dotsenko, Vladimir Rings and Algebras Analysis of PDEs Probability 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. |
| title | Novikov algebras and multi-indices in regularity structures |
| topic | Rings and Algebras Analysis of PDEs Probability |
| url | https://arxiv.org/abs/2311.09091 |