|
We begin by reviewing the main results of the theory of finite dimensional Lie algebras. We continue by considering the class of split Lie algebras of arbitrary dimension. As a generalization, we study the structure of weight modules over< split Lie algebras. We show that under certain conditions a split Lie algebra is a direct sum of ideals and a weight module is a direct sum of (weight) submodules in such a way that for any submodule there exists a unique satisfying that their action is nonzero. Also, it is shown that the above decomposition of the weight submodule is by means of the family of its minimal submodules, each one being a simple (weight) submodule.
|
