The rational homotopy Lie algebra of classifying spaces for formal two-stage spaces

AbstractWe compute the center and nilpotency of the graded Lie algebra π∗(ΩBaut1(X))⊗Q for a large class of formal spaces X. The latter calculation determines the rational homotopical nilpotency of the space of self-equivalences aut1(X) for these X. Our results apply, in particular, when X is a complex or symplectic flag manifold