Differential graded algebras with divided powers and homotopy Lie algebras

Given a commutative ring R and a quotient module R/m, we study the structure of differential graded algebra with divided powers that the resolution of R/m can possess. We provide a construction of such a resolution by making use of symmetric tensors, which does not require a Noetherian assumption on R. We then apply those results to study the homotopy Lie algebra associated to a the pair (R,R/m), and then investigate in more details the complete intersection case.