Jiménez Rodríguez, María JoséReal Jurado, Pedro2021-09-152021-09-152001Jiménez Rodríguez, M.J. y Real Jurado, P. (2001). “Coalgebra” Structures on 1-Homological Models for Commutative Differential Graded Algebras. En CASC 2001: 4th International Workshop on Computer Algebra in Scientific Computing (347-361), Konstanz, Germany: Springer.978-3-642-62684-5https://hdl.handle.net/11441/125773In [3] “small” 1-homological model H of a commutative differential graded algebra is described. Homological Perturbation Theory (HPT) [7-9] provides an explicit description of an A∞-coalgebra structure (Δ1,Δ2,Δ3,...) of H. In this paper, we are mainly interested in the determination of the map Δ2 : H - H H ⊗ H as a first step in the study of this structure. Developing the techniques given in [20] (inversion theory), we get an important improvement in the computation of Δ2 with regard to the first formula given by HPT. In the case of purely quadratic algebras, we sketch a procedure for giving the complete Hopf algebra structure of its 1-homology.application/pdf15engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Hopf AlgebraHomogeneous ElementPolynomial AlgebraAlgebra GeneratorHomological Algebrainfo:eu-repo/semantics/conferenceObjectinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1007/978-3-642-56666-0_26