Equivariant rational homotopy theory as a closed model category

Abstract

In this note we present a variant of the algebraization of equivariant rational homotopy theory. For a finite group G, let øO( G) be the category of its canonical orbits. We prove that the category øO( G)- DGA O of øO( G)-differential graded algebras over the rationals is a closed model category. Then, by means of the equivariant KS-minimal models constructed in this paper, we show that the homotopy category of øO( G)- DGA O is equivalent to the rational homotopy category of øO( G)-simplicial sets provided G is a Hamiltonian group.