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arXiv · 2605.29878

Differential graded Hopf algebra structure on free symmetric cosimplicial operads

Calvin Tcheka·Batkam Mbatchou V. Jacky III·Guy R. Biyogmam
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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.

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Calvin Tcheka, Batkam Mbatchou V. Jacky III, Guy R. Biyogmam. 2026-05-28. Differential graded Hopf algebra structure on free symmetric cosimplicial operads. https://arxiv.org/abs/2605.29878

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