ABSTRACT
This chapter shows how to obtain, starting from a basis of the dynamical Lie algebra L, bases of its Abelian part and of the simple ideals of its semisimple part. This gives the decomposition of uncontrollable dynamics The chapter discusses decomposition more in depth and, with the help of some notions of representation theory, and in particular of Schur lemma, and shows that in a special basis, the dynamical Lie algebra takes the form of a tensor product. Schur lemma is one of the most useful tools in representation theory. It shows that any irreducible representation of a product group has a tensor product structure.
