A Lie group is a differentiable manifold that has the structure of a group and that satisfies the additional condition that the group operations of multiplication and inversion are continuous.

compact Lie group | continuous group | group | Lie algebra | Lie groupoid | Lie-type group | Lorentz group | nil geometry | orthogonal group | semisimple Lie group | smooth manifold | Sol geometry | tangent space | vector field

graduate school level