the search for the simplification and unification of some of the proofs of the standard results on faithfull representations of Lie groups. In this respect, in the introduction to [@kn:mostow] and after describing the main results of [@kn:homolie] the author writes:

Indeed, in [@kn:homolie Section 3], short new proofs of the following three classical and important theorems are presented. E. Cartan’s theorem on the existence of a faithful representation of a simply connected solvable Lie group, that is unipotent in a maximal normal nilpotent subgroup; Goto’s theorem on the existence of a faithful represention of a connected Lie group $G$ provided we know the existence of a representation for a maximal semisimple subgroup together with additional topological conditions on the radical of the commutator subgroup of $G$, and Malcev theorem that guarantees the existence of a faithfull representation of a connected Lie group once we know that such a representation exists for the radical of $G$ and for a maximal semisimple analytic subgroup of $G$.

Observability and geometry, observability and invariant theory
==============================================================

Observability and geometry {#subsection:obsgeo}
--------------------------

One of the more interesting results of ERA is the discovery of the relationship between the extension of the representations from $H$ 