Weighted differential ($q$-tri)dendriform algebras
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917698810675200 |
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| author | Zhang, Yuanyuan Zhang, Huhu Wu, Tingzeng Gao, Xing |
| author_facet | Zhang, Yuanyuan Zhang, Huhu Wu, Tingzeng Gao, Xing |
| contents | In this paper, we first introduce a weighted derivation on algebras over an operad $\cal P$, and prove that for the free $\cal P$-algebra, its weighted derivation is determined by the restriction on the generators. As applications, we propose the concept of weighted differential ($q$-tri)dendriform algebras and study some basic properties of them. Then Novikov-(tri)dendriform algebras are initiated, which can be induced from differential ($q$-tri) dendriform of weight zero. Finally, the corresponding free objects are constructed, in both the commutative and noncommutative contexts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_12871 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weighted differential ($q$-tri)dendriform algebras Zhang, Yuanyuan Zhang, Huhu Wu, Tingzeng Gao, Xing Rings and Algebras 16W99, 16S10, 13P10, 08B20, In this paper, we first introduce a weighted derivation on algebras over an operad $\cal P$, and prove that for the free $\cal P$-algebra, its weighted derivation is determined by the restriction on the generators. As applications, we propose the concept of weighted differential ($q$-tri)dendriform algebras and study some basic properties of them. Then Novikov-(tri)dendriform algebras are initiated, which can be induced from differential ($q$-tri) dendriform of weight zero. Finally, the corresponding free objects are constructed, in both the commutative and noncommutative contexts. |
| title | Weighted differential ($q$-tri)dendriform algebras |
| topic | Rings and Algebras 16W99, 16S10, 13P10, 08B20, |
| url | https://arxiv.org/abs/2406.12871 |