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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2311.03808 |
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| _version_ | 1866910923435802624 |
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| author | Manchon, Dominique Regeiba, Hedi Rjaiba, Imen Vargas, Yannic |
| author_facet | Manchon, Dominique Regeiba, Hedi Rjaiba, Imen Vargas, Yannic |
| contents | We study algebraic structures on the free commutative twisted algebra generated by a positive operad $\mathbf q$, in the framework of vector species. Given a nonunital commutative twisted algebra structure $μ$ on $\mathbf q$, we introduce the notion of $μ$-compatible operad structure, leading to a nonunital operad structure on $\mathbf E \circ \mathbf q$, where $\mathbf E$ stands for the exponential species. Next, we define nested pre-Lie operads (NPL-operads), a weak form of the notion of operad, in which the nested associativity axiom is weakened down to a nested pre-Lie condition. This structure is new up to our knowledge. Several constructions of NPL-operads are presented. Finally, we define algebras over a NPL-operad, based on the notion of polynomial functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_03808 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the free commutative monoid over a positive operad Manchon, Dominique Regeiba, Hedi Rjaiba, Imen Vargas, Yannic Combinatorics 18M80, 70G65, 47H60 We study algebraic structures on the free commutative twisted algebra generated by a positive operad $\mathbf q$, in the framework of vector species. Given a nonunital commutative twisted algebra structure $μ$ on $\mathbf q$, we introduce the notion of $μ$-compatible operad structure, leading to a nonunital operad structure on $\mathbf E \circ \mathbf q$, where $\mathbf E$ stands for the exponential species. Next, we define nested pre-Lie operads (NPL-operads), a weak form of the notion of operad, in which the nested associativity axiom is weakened down to a nested pre-Lie condition. This structure is new up to our knowledge. Several constructions of NPL-operads are presented. Finally, we define algebras over a NPL-operad, based on the notion of polynomial functions. |
| title | On the free commutative monoid over a positive operad |
| topic | Combinatorics 18M80, 70G65, 47H60 |
| url | https://arxiv.org/abs/2311.03808 |