Lie Group

A continuous Group with an infinite number of elements such that the parameters of a product element are Analytic Functions. Lie groups are also $C^\infty$ Manifolds with the restriction that the group operation maps a $C^\infty$ map of the Manifold into itself. Examples include ${\it O}_3$, ${\it SU}(n)$, and the Lorentz Group.

See also Compact Group, Lie Algebra, Lie Groupoid, Lie-Type Group, Nil Geometry, Sol Geometry

References

Arfken, G. ``Infinite Groups, Lie Groups.'' Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, p. 251-252, 1985.

Chevalley, C. Theory of Lie Groups. Princeton, NJ: Princeton University Press, 1946.

Knapp, A. W. Lie Groups Beyond an Introduction. Boston, MA: Birkhäuser, 1996.

Lipkin, H. J. Lie Groups for Pedestrians, 2nd ed. Amsterdam, Netherlands: North-Holland, 1966.