Differential graded Hopf algebra structure on free symmetric cosimplicial operads
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911728354197504 |
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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 |