Weighted differential (-tri)dendriform algebras
arXiv:2406.12871
Abstract
In this paper, we first introduce a weighted derivation on algebras over an operad , and prove that for the free -algebra, its weighted derivation is determined by the restriction on the generators. As applications, we propose the concept of weighted differential (-tri)dendriform algebras and study some basic properties of them. Then Novikov-(tri)dendriform algebras are initiated, which can be induced from differential (-tri) dendriform of weight zero. Finally, the corresponding free objects are constructed, in both the commutative and noncommutative contexts.
26 pages. arXiv admin note: substantial text overlap with arXiv:2305.19609