Lie group

In mathematics, a Lie group is an analytic real or complex manifold that is also a group such that the group operations multiplication and inversion are analytic maps. Lie groups are important in mathematical analysis, physics and geometry because they serve to describe the symmetry of analytical structures. They were introduced by Sophus Lie in 1870 in order to study symmetries of differential equations.

Types of Lie groups

One classifies Lie groups regarding their algebraic properties (simple, semisimple, solvable, nilpotent, abelian), their connectedness (connected or simply connected) and their compactness.

Related Topics:
Simple - Semisimple - Solvable - Nilpotent - Abelian - Connectedness - Simply connected - Compactness

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