Induced structures of operated algebras with applications to multi-Novikov algebras
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866912975394177024 |
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| author | Guo, Li Wang, Xiaoyan Zhang, Huhu |
| author_facet | Guo, Li Wang, Xiaoyan Zhang, Huhu |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_19553 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Induced structures of operated algebras with applications to multi-Novikov algebras Guo, Li Wang, Xiaoyan Zhang, Huhu Category Theory Rings and Algebras 18M60, 17A30, 18M70, 12H05, 17D25 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. |
| title | Induced structures of operated algebras with applications to multi-Novikov algebras |
| topic | Category Theory Rings and Algebras 18M60, 17A30, 18M70, 12H05, 17D25 |
| url | https://arxiv.org/abs/2603.19553 |