  Lie bialgebras occur as the principal objects in the infinitesimalisation of
the theory of quantum groups - the semi-classical theory. Their relationship
with the quantum theory has made available some new tools that we can apply to
classical questions. In this paper, we study the simple complex Lie algebras
using the double-bosonisation construction of Majid. This construction
expresses algebraically the induction process given by adding and removing
nodes in Dynkin diagrams, which we call Lie induction.
  We first analyse the deletion of nodes, corresponding to the restriction of
adjoint representations to subalgebras. This uses a natural grading associated
to each node. We give explicit calculations of the module and algebra
structures in the case of the deletion of a single node from the Dynkin diagram
for a simple Lie (bi-)algebra.
  We next consider the inverse process, namely that of adding nodes, and give
some necessary conditions for the simplicity of the induced algebra. Finally,
we apply these to the exceptional series of simple Lie algebras, in the context
of finding obstructions to the existence of finite-dimensional simple complex
algebras of types E9, F5 and G3. In particular, our methods give a new point of
view on why there cannot exist such an algebra of type E9.
