# Lie group

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Lie groups provide a natural model for the concept of continuous symmetry, a celebrated example of which is the rotational symmetry in three dimensions (given by the special orthogonal group ${\displaystyle {\text{SO}}(3)}$). Lie groups are widely used in many parts of modern mathematics and physics.
Lie groups were first found by studying matrix subgroups ${\displaystyle G}$ contained in ${\displaystyle {\text{GL}}_{n}(\mathbb {R} )}$ or ${\displaystyle {\text{GL}}_{n}(\mathbb {C} )}$, the groups of ${\displaystyle n\times n}$ invertible matrices over ${\displaystyle \mathbb {R} }$ or ${\displaystyle \mathbb {C} }$. These are now called the classical groups, as the concept has been extended far beyond these origins. Lie groups are named after Norwegian mathematician Sophus Lie (1842–1899), who laid the foundations of the theory of continuous transformation groups. Lie's original motivation for introducing Lie groups was to model the continuous symmetries of differential equations, in much the same way that finite groups are used in Galois theory to model the discrete symmetries of algebraic equations.