Induced structures of operated algebras with applications to multi-Novikov algebras

Li Guo; Xiaoyan Wang; Huhu Zhang

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arXiv · 2603.19553

Induced structures of operated algebras with applications to multi-Novikov algebras

Li Guo·Xiaoyan Wang·Huhu Zhang

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Abstract

We provide a general notion of induced structures of operated algebras in the context of unary-binary operads. This notion fully captures the binary quadratic relations encoded by a unary-binary operad, thereby unifying and formalizing the various constructions that have appeared in the literature under the informal term of ``induced structures''. As an application, we show that the Novikov algebra and the recently introduced multi-Novikov algebra are the induced structures of the differential commutative algebra and the multi-differential commutative algebra respectively. We also explicitly determine the induced structure of the noncommuting multi-differential commutative algebra.

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BibTeX RIS

Li Guo, Xiaoyan Wang, Huhu Zhang. 2026-03-20. Induced structures of operated algebras with applications to multi-Novikov algebras. https://arxiv.org/abs/2603.19553

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