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oai:riuma.uma.es:10630/390282026-02-03T11:17:52Zcom_10630_2254col_10630_37953

On Differential Hopf Algebras and B∞ Algebras Gálvez-Carrillo, Imma Ronco, María Tonks, Andrew Peter Algebra diferencial Hopf, Algebras de B∞-algebra A∞-algebra Differential Hopf algebra Quasi-shuffle We establish a structure theorem analogous to the classical result of Milnor and Moore: any differential graded (not necessarily co commutative) Hopf algebra H that is cofree as a coalgebra carries an underlying B∞ algebra structure that restricts to the subspace of prim itives, and conversely H may be recovered via a universal enveloping 2-associative differential algebra. This extends the work of Loday and Ronco (J. reine angew. Math. 592: 123–155, 2006) where the ungraded non-differential case was treated, and only the multibrace part of the B∞ structure was found. We show that the multibrace algebras of Loday and Ronco (J. reine angew. Math. 592: 123–155, 2006) originate from twistings of quasi-trivial structures, complementing the work of Markl (J. Homotopy Relat. Struct. 10, 637–667 (2015)) on the A∞ structure underlying any algebra with a square-zero endomorphism. In this frame work we can prove the multibrace and A∞ algebras are compatible and provide the appropriate B∞ algebra for the structure theorem. Funding for open access charge: Universidad de Málaga / CBUA 2025-06-17T11:43:59Z 2025-06-17T11:43:59Z 2025-06-05 journal article VoR Gálvez-Carrillo, I., Ronco, M. & Tonks, A. On Differential Hopf Algebras and Algebras. Mediterr. J. Math. 22, 93 (2025). https://doi.org/10.1007/s00009-025-02863-w https://hdl.handle.net/10630/39028 10.1007/s00009-025-02863-w eng Atribución 4.0 Internacional http://creativecommons.org/licenses/by/4.0/ open access application/pdf Springer Nature