\(S\)-module and the new Massey-product (Q1355613)

Let \(H\) be a commutative coassociative Hopf algebra over a field \(\mathbb{K}\) and \(R\) be the cobar construction on \(H\). The author defines an \(S\)-module as a DG-bimodule \(M\) over the DG-algebra \(R\) equipped with a homotopy \(S:R\otimes M\to M\) such that \((S\circ d+d\circ S)(a\otimes m)=[a,m]\) and each \(S(a,-)\) is a biderivation. This permits to consider the Massey products defined in [J. Algebra 183, No. 2, 378-395 (1996; Zbl 0859.57041)] as obstruction classes. He applies his main result concerning the induced map in cohomology by the inclusion of a sub-Hopf algebra to the \(E_2\)-term of the classical Adams spectral sequence.