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Lie algebras
Topics in Non commutative algebraic geometry and congruent zeta functions (Part VI). Lie algebras and their enveloping algebras
Yoshifumi Tsuchimoto
Lie algebras
Representations of a Lie algebra
Poincaré-Birkoff-Witt Theorem
Jordan-Chevalley decomposition of a square matrix
Existence and uniqueness of Jordan-Chevalley decomposition
-rationality
generalities in finite dimensional Lie algebras
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
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
Bibliography
About this document ...
2009-03-06
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-rationality