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== Relation to Lie groups ==
{{main|Lie group–Lie algebra correspondence}}
[[Image:Image Tangent-plane.svg|thumb| the tangent space of a [[sphere]] at a point <math>x</math>. If <math>x</math> is the identity element, then the tangent space is also a Lie Algebra]]
Although Lie algebras are often studied in their own right, historically they arose as a means to study [[Lie group]]s.
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