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.

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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.

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Real: The word "real" has many different meanings:...

Complex: A complex is a whole that comprehends a number of parts, especially one with interconnected or mutually related parts.In psychology, a complex is a group of mental factors that are unconsciously associated by the individual with a particular subject and influence the individual's attitude and behavi...

Group: The term group can refer to several concepts:...

Lie group related Images and Photos (experimental)

Group Effort: Rugby	The Group	Red - Group	Blue - Group
Wolf Group	Vivid Group	Sonic - Group	Skins - Group
Vivid Group	Hedley Group	Group Cactus Cutout	Watchmen - Group