Differential graded Hopf algebra structure on free symmetric cosimplicial operads

Fuente: arXiv
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Autori principali: Tcheka, Calvin, Jacky III, Batkam Mbatchou V., Biyogmam, Guy R.
Natura: Preprint
Pubblicazione: 2026
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author Tcheka, Calvin
Jacky III, Batkam Mbatchou V.
Biyogmam, Guy R.
author_facet Tcheka, Calvin
Jacky III, Batkam Mbatchou V.
Biyogmam, Guy R.
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2605_29878
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Differential graded Hopf algebra structure on free symmetric cosimplicial operads
Tcheka, Calvin
Jacky III, Batkam Mbatchou V.
Biyogmam, Guy R.
Rings and Algebras
Algebraic Topology
16N60, 18N50, 18G31, 19D23, 18M05, 57T99
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.
title Differential graded Hopf algebra structure on free symmetric cosimplicial operads
topic Rings and Algebras
Algebraic Topology
16N60, 18N50, 18G31, 19D23, 18M05, 57T99
url https://arxiv.org/abs/2605.29878