Editing Geometry (section)

==Classification of Lie algebras and Dykin diagrams==
[https://www.youtube.com/watch?v=Vlbcd_lPNMA&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=14 Lecture 14]

complex Lie algebras; abelian Lie algebras; the trivial Lie algebra; ideal of a Lie algebra; trivial ideals; simple and semi-simple Lie algebras; derived subalgebra; solvability; direct and semi-direct sum of Lie algebras; Levi's theorem on the decomposition of finite-dimensional complex Lie algebras; adjoint map and ad; proof that ad is a Lie algebra homomorphism; Killing form; proof of the invariance (or associativity, or anti-symmetry) of the Killing form; a Lie algebra is semi-simple if and only if the Killing is non-degenerate; structure constants; components of adjoint maps and the Killing form in terms of the structure constants; Cartan subalgebra, rank of a Lie algebra and Cartan-Weyl basis; roots and fundamental roots; proof that the restriction of the Killing form on a Cartan subalgebra is a pseudo inner product; real inner product; length and angle between roots; Weyl transformations and Weyl group; Cartan matrix; bond number; Dynkin diagrams and classification of finite-dimensional semi-simple complex Lie algebras.