Differential graded Hopf algebra structure on free symmetric cosimplicial operads
math.RAmath.AT2026-05v1license
Abstract
Motivated by the recent work of Batkam-Tcheka on pointed multiplicative operads, we construct in this paper new chain complex algebras and two distinct bicomplex algebra structures on a free symmetric connected multiplicative differential graded operad. Furthermore, we focus on the non-differential graded case and construct a differential graded Hopf algebra structure using the odot product together with an analogue of the Alexander-Whitney homomorphism and a compatible differential. As a consequence, we extend the Malvenuto-Reutenauer result by showing that every free symmetric connected multiplicative operad naturally carries a differential graded Hopf algebra structure.
Cite
@article{arxiv.2605.29878,
title = {Differential graded Hopf algebra structure on free symmetric cosimplicial operads},
author = {Calvin Tcheka and Batkam Mbatchou V. Jacky and Guy R. Biyogmam},
journal= {arXiv preprint arXiv:2605.29878},
year = {2026}
}