Orthogonal Involutive Lie Algebras

This chapter is mainly algebraic, and devoted to the discussion of a class of real Lie algebras which we call orthogonal involutive. Their interest stems from two sources. On the one hand, these are the Lie algebras of the groups of isometries of Riemannian symmetric spaces and this chapter, in particular §1, may to some extent be viewed as an algebraic preliminary to the study of symmetric spaces. The reader mainly interested in those spaces may well go over directly to Chapter III, and come back to the present one whenever needed.