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arXiv · 2603.16766

General multi-Novikov algebras, multi-differential algebras and their free constructions

Xiaoyan Wang·Li Guo·Huhu Zhang
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Abstract

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.

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Xiaoyan Wang, Li Guo, Huhu Zhang. 2026-03-17. General multi-Novikov algebras, multi-differential algebras and their free constructions. https://arxiv.org/abs/2603.16766

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