English

Weighted differential ($q$-tri)dendriform algebras

Rings and Algebras 2024-06-21 v1

Abstract

In this paper, we first introduce a weighted derivation on algebras over an operad P\cal P, and prove that for the free P\cal P-algebra, its weighted derivation is determined by the restriction on the generators. As applications, we propose the concept of weighted differential (qq-tri)dendriform algebras and study some basic properties of them. Then Novikov-(tri)dendriform algebras are initiated, which can be induced from differential (qq-tri) dendriform of weight zero. Finally, the corresponding free objects are constructed, in both the commutative and noncommutative contexts.

Keywords

Cite

@article{arxiv.2406.12871,
  title  = {Weighted differential ($q$-tri)dendriform algebras},
  author = {Yuanyuan Zhang and Huhu Zhang and Tingzeng Wu and Xing Gao},
  journal= {arXiv preprint arXiv:2406.12871},
  year   = {2024}
}

Comments

26 pages. arXiv admin note: substantial text overlap with arXiv:2305.19609

R2 v1 2026-06-28T17:10:47.369Z