Algèbres de Lie de dérivations de certaines algèbres pures

Abstract

Let E ( X ) be the H -space of homotopy self-equivalences which are homotopic to the identity of a homogeneous Kähler manifold with maximal rank. The Lie algebra of derivations of a pure differential graded algebra with zero homotopy Euler characteristic allows us to use Sullivan's minimal model to study the rational homotopy theory of E ( X ). As an application we compute dim (π ∗ (E(X)) ⊗ Q ) in the case when X is a certain flag manifold.