- Ideals of Lie algebras
- Simple, semisimple, solvable, and nilpotent Lie algebras: definition
- The radicals of Lie algebras
- Theorem of Engel
- Ideals of
- Ideals of .
- Invariant bilinear forms and Killing forms

- Theorem of Iwasawa
- Cartan's criterion for solvability(Ccs)
- Cartan's criterion for semisimplicity
- examples
- Weyl's theorem on complete reducibility
- Semi direct products of Lie algebras.
- Levi decomposition
- Abstract Jordan Chevalley decomposition

2009-03-06