Disconnected Equivariant Rational Homotopy Theory

We present a variant of the disconnected equivariant rational homotopy theory to complete the result shown in [8]. For a finite group G let O(G) be the category of its canonical orbits. We prove that the category O(G)∫-DGA∧Q of O(G)∫S-complete differential graded algebras over the rationals is a closed model category, where S runs over all O(G)-sets. Then, by means of the equivariant KS-minimal models, we show that the homotopy category of O(G)∫-DGA∧Q is equivalent to the rational homotopy category of G-nilpotent disconnected simplicial sets provided G is a finite Hamiltonian group.