## "Coalgebra" Structures on 1-Homological Models for Commutative Differential Graded Algebras

### BibTeX

@MISC{Jiménez_"coalgebra"structures,

author = {M.J. Jiménez and P. Real},

title = {"Coalgebra" Structures on 1-Homological Models for Commutative Differential Graded Algebras},

year = {}

}

### OpenURL

### Abstract

In [3] "mall" 1-homological model H of a commutative differential graded algebra is described. Homological Perturbation Theory (HPT) [7-9] provides an explicit description of an A1-coalgebra structure ( 1 ; 2 ; 3 ; : : :) of H. In this paper, we are mainly interested in the determination of the map 2 : 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 2 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.