Broken symmetry of lie groups of transformation generating general relativistic theories of gravitation

Intransitive Lie groups of transformations have invariant varieties which in suitable cases can be considered as space-times of a universe. The physical laws in the latter are expressed in terms of group theoretical notions. Theorems on the coincidences of group trajectories and geodesics are derived. The groups of linear transformations of the space of basis vectors are used as gauge groups to break the symmetry of the group of transformations and of their natural metric. It is shown that in case of the de Sitter group and its adjoint group as gauge group, one obtains in this way general relativistic theories of gravitation, especially Einstein's theory. More general aspects of the formalism are discussed.Article written in memoriam of B. Jouvet of the Collège de France