= Representation theory of Lie groups
{wiki=Representation_theory_of_Lie_groups}
Representation theory of Lie groups is a branch of mathematics that studies how Lie groups can be represented as groups of transformations on vector spaces. More formally, a representation of a Lie group \\( G \\) is a homomorphism from \\( G \\) to the general linear group GL(V) of invertible linear transformations on a vector space \\( V \\). This allows one to study properties of the group \\( G \\) through linear algebra and the geometry of vector spaces.
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