RT Journal Article
T1 On Differential Hopf Algebras and B∞ Algebras
A1 Gálvez-Carrillo, Imma
A1 Ronco, María
A1 Tonks, Andrew Peter
K1 Algebra diferencial
K1 Hopf, Algebras de
AB We establish a structure theorem analogous to the classicalresult of Milnor and Moore: any differential graded (not necessarily co commutative) Hopf algebra H that is cofree as a coalgebra carries anunderlying B∞ algebra structure that restricts to the subspace of prim itives, and conversely H may be recovered via a universal enveloping2-associative differential algebra. This extends the work of Loday andRonco (J. reine angew. Math. 592: 123–155, 2006) where the ungradednon-differential case was treated, and only the multibrace part of theB∞ structure was found. We show that the multibrace algebras of Lodayand Ronco (J. reine angew. Math. 592: 123–155, 2006) originate fromtwistings of quasi-trivial structures, complementing the work of Markl(J. Homotopy Relat. Struct. 10, 637–667 (2015)) on the A∞ structureunderlying any algebra with a square-zero endomorphism. In this frame work we can prove the multibrace and A∞ algebras are compatible andprovide the appropriate B∞ algebra for the structure theorem.
PB Springer Nature
YR 2025
FD 2025-06-05
LK https://hdl.handle.net/10630/39028
UL https://hdl.handle.net/10630/39028
LA eng
NO 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
NO Funding for open access charge: Universidad de Málaga / CBUA
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 21 ene 2026