Title: Divided power algebras over an operad

Abstract: Divided power algebras were introduced by Cartan in the study of the homology of Eilenberg-MacLane spaces. The more general notion of divided power algebra over an operad was introduced by Fresse in the study of the homotopy of simplicial algebras over an operad. The aim of this talk is to characterise divided power algebras over an operad as defined by Fresse in terms of monomial operations and relations, following the classical definition of Cartan. We will establish such a characterisation, and show some examples of refinement obtained by fixing the operad, and the characteristic of the base field.