On the structure of real transitive lie algebras

In this paper, we examine some of the ways in which abstract algebraic objects in a transitive Lie algebra L are expressed geometrically in the action of each transitive Lie pseudogroup T associated to L. We relate those chain decompositions of T which result from considering T-invariant foliations to Jordan-Holder sequences (in the sense of Cartan and Guillemin) for L. Local coordinates are constructed which display the nature of the partial differential equations defining T; in particular, locally homogeneous pseudocomplex structures (also called CR-structures) are associated to the nonabelian quotients of complex type in a Jordan-Holder sequence for L.