General multi-Novikov algebras, multi-differential algebras and their free constructions
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908894480039936 |
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| author | Wang, Xiaoyan Guo, Li Zhang, Huhu |
| author_facet | Wang, Xiaoyan Guo, Li Zhang, Huhu |
| contents | Motivated by the recent development of noncommutative Novikov algebras and multi-Novikov algebras from the study of regularity structures of stochastic PDEs, this paper gives a general approach to study various multi-Novikov algebras and multi-differential algebras, with close connection with Poisson algebras. The construction of S. Gelfand of Novikov algebras from differential commutative algebras is generalized to this context. Free noncommuting multi-Novikov algebras are constructed from typed decorated rooted trees and from noncommuting multi-differential polynomials with populated conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_16766 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | General multi-Novikov algebras, multi-differential algebras and their free constructions Wang, Xiaoyan Guo, Li Zhang, Huhu Rings and Algebras Combinatorics Quantum Algebra 17A30, 12H05, 17D25, 17B63 Motivated by the recent development of noncommutative Novikov algebras and multi-Novikov algebras from the study of regularity structures of stochastic PDEs, this paper gives a general approach to study various multi-Novikov algebras and multi-differential algebras, with close connection with Poisson algebras. The construction of S. Gelfand of Novikov algebras from differential commutative algebras is generalized to this context. Free noncommuting multi-Novikov algebras are constructed from typed decorated rooted trees and from noncommuting multi-differential polynomials with populated conditions. |
| title | General multi-Novikov algebras, multi-differential algebras and their free constructions |
| topic | Rings and Algebras Combinatorics Quantum Algebra 17A30, 12H05, 17D25, 17B63 |
| url | https://arxiv.org/abs/2603.16766 |