Aspects of Lie Theory
The foundation of Lie theory is the exponential map relating Lie algebra to Lie group. Structure is captured in Root systems and root data. Lie theory is frequently built upon a study of the classical linear algebraic groups. Special branches include Weyl groups, Coxeter groups, and buildings. The classical subject has been extended to Groups of Lie type.
In 1900 David Hilbert challenged Lie theorists with his Fifth Problem presented at the International Congress of Mathematicians in Paris.
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