Good gradings of simple Lie algebras

This thesis aims to study the good gradings of simple finite-dimensional Lie algebras. The Dynkin grading is given as an example of good Z-grading of a semisimple Lie algebra. The main properties of a good Z-grading of a semisimple Lie algebra are proved and all good Z-gradings of gl(n), the Lie algebra of all matrices of order n, are classified. Finally, we extend the definition of good gradings to Lie superalgebras and start studying the good gradings of the Cartan superalgebra W(n). The case of W(2) and W(3) are analyzed.