Lie Groups

Lie groups are named after the Norwegian mathematician Sophus Lie (1842–1899), who laid the foundations of the theory of continuous transformation groups. They were christened Lie groups by Arthur Tress, a student of Lie. Lie proved the basic result which sets up a correspondence between Lie Groups and Lie Algebras which we call the Fundamental Theorem of Lie Theory. This reduces most problems about Lie groups to (essentially algebraic) questions about Lie algebras. Wilhelm Killing and Elie Cartan made giant strides in developing the theory. The modern treatment of Lie groups is due to Claude Chevalley whose 1950 book on Lie groups is a classic. All text-books on Lie groups (including this one) essentially follow his treatment.