Editing Differential geometry (section)

=== Lie groups ===
A [[Lie group]] is a [[Group (mathematics)|group]] in the category of smooth manifolds. Beside the algebraic properties this enjoys also differential geometric properties. The most obvious construction is that of a Lie algebra which is the tangent space at the unit endowed with the Lie bracket between left-invariant [[vector field]]s. Beside the structure theory there is also the wide field of [[representation of a Lie group|representation theory]].