On the minimality of Anick's resolution, with application to an algebra of cohomology operations (Q1911334)

Let \(k\) be a field, \(G\) an augmented \(k\)-algebra, generated by a set \(S\). In his paper ``Homology of associative algebras'' [Trans. Am. Math. Soc. 296, 641-659 (1986; Zbl 0598.16028)] \textit{D. J. Anick} deduced a certain projective \(G\)-resolution of \(k\), using a grading \(e:S\to\mathbb{N}\), an ordering of \(S\) such that \(e^{-1} (n)\) is well ordered for all \(n \in \mathbb{N}\), and the notion of an obstruction in the free monoid over \(S\). Here, the author proves the minimality of Anick's resolution under the assumption that \(S\) is a minimal set of generators contained in the augmentation ideal and that all obstructions are monomials of length 2.