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generalities in finite dimensional Lie algebras

Subsections

Ideals of Lie algebras
Simple, semisimple, solvable, and nilpotent Lie algebras: definition
The radicals of Lie algebras
Theorem of Engel
Ideals of $\mathfrak{gl}_n(k)$
Ideals of $\mathfrak{sl}_n(k)$ .
Invariant bilinear forms and Killing forms
- functoriality of 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