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.

Related Topics:
Mathematics - Real - Complex - Manifold - Group - Analytic maps - Mathematical analysis - Physics - Geometry - Sophus Lie - 1870

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While the Euclidean space Rn is a real Lie group (with ordinary vector addition as the group operation), more typical examples are given by matrix Lie groups, i.e. groups of invertible matrices (under matrix multiplication). For instance, the group SO(3) of all rotations in 3-dimensional space is a matrix Lie group. For a more complete list of examples see the table of Lie groups and list of simple Lie groups.

Related Topics:
Euclidean space - Invertible - Matrices - Matrix multiplication - SO(3) - Rotation - Table of Lie groups - List of simple Lie groups

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