ORTHOGONAL LIE-ALGEBRAS - ORTHOGONAL MODU LES

We continue our study of orthogonal Lie algebras, i.e. Lie algebras wh ich support an invariant scalar product. We first show that a Lie alge bra has a non degenerate invariant bilinear form iff adjoint and coadj oint representations are isomorphic. We study the space of all invaria nt bilinear forms on an orthogonal algebra. In a second part we study orthogonal modules and give a complete description of the double exten sion process which allows to construct all orthogonal modules ; we giv e examples and raise the question of existence of non-isomorphic ortho gonal structures on a given orthogonal Lie algebra.