Free weighted differential ($q$-tri)dendriform algebras

Abstract

In the present paper, we propose the concepts of weighted differential ($q$-tri)dendriform algebras and give some basic properties of them. The corresponding free objects are constructed, in both the commutative and noncommutative contexts.

arXiv commentThis paper is just the old version of the arXiv:2406.12871. Sorry I forget I have uploaded it before. So it would be great to turn arXiv:2305.19609 to version 1 of the newest arXiv:2406.12871