A model category structure for equivariant algebraic models

Abstract

In the equivariant category of spaces with an action of a finite group, algebraic ‘minimal models’ exist which describe the rational homotopy for G G -spaces which are 1-connected and of finite type. These models are diagrams of commutative differential graded algebras. In this paper we prove that a model category structure exists on this diagram category in such a way that the equivariant minimal models are cofibrant objects. We show that with this model structure, there is a Quillen equivalence between the equivariant category of rational G G -spaces satisfying the above conditions and the algebraic category of the models.