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arXiv · 2406.12871

Weighted differential ($q$-tri)dendriform algebras

Yuanyuan Zhang·Huhu Zhang·Tingzeng Wu·Xing Gao
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Abstract

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.

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Yuanyuan Zhang, Huhu Zhang, Tingzeng Wu, Xing Gao. 2024-04-28. Weighted differential ($q$-tri)dendriform algebras. https://arxiv.org/abs/2406.12871

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