The classification of locally finite split simple Lie algebras

One of the great early achievements in Lie theory is the classification of the finite dimensional simple complex Lie algebras by W. Killing and E. Cartan. More than 50 years later new aspects were added to this classification by the theory of Coxeter groups and the visualization of the classification in terms of Dynkin diagrams. Furthermore Serre’s description of the simple Lie algebras by generators and relations provided a direct way to construct the Lie algebras from the Cartan matrix corresponding to the choice of a root base, i.e., a system of simple roots.

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