Differential graded algebras with divided powers and homotopy Lie algebras

Abstract: Given a commutative ring $R$ and a quotient module $R/\mathfrak{m}$, we study the structure of differential graded algebra with divided powers that the resolution of $R/\mathfrak{m}$ 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 $(R,R/\mathfrak{m})$, and then investigate in more details the complete intersection case.