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# and Lie
# REDIRECT Lie algebra
# Vector fields on any smooth manifold M can be thought of as derivations X of the ring of smooth functions on the manifold, and therefore form a Lie algebra under the Lie bracket = XY − YX, because the Lie bracket of any two derivations is a derivation.
# If G is any group acting smoothly on the manifold M, then it acts on the vector fields, and the vector space of vector fields fixed by the group is closed under the Lie bracket and therefore also forms a Lie algebra.
# We apply this construction to the case when the manifold M is the underlying space of a Lie group G, with G acting on G = M by left translations L < sub > g </ sub >( h ) = gh.
# Any tangent vector at the identity of a Lie group can be extended to a left invariant vector field by left translating the tangent vector to other points of the manifold.
# REDIRECT Lie group
# Lie or commit perjury
# Let Sleeping Corpses Lie ( original title: Non si deve profanare il sonno dei morti ; also known as The Living Dead at Manchester Morgue, Don't Open the Window ) — passed with 2 minutes pre-cut in 1985 ; re-released uncut in 2002
# " The Lie " 1: 19
# the compact form, sp ( n ), which is the Lie algebra of Sp ( n ),
# the algebras, sp ( p, n − p ), which are the Lie algebras of Sp ( p, n − p ), the indefinite signature equivalent to the compact form,
# the normal form ( or split form ), sp ( 2n, R ), which is the Lie algebra of Sp ( 2n, R ).
# " Sun Don't Lie " – 6: 29
# " On the Lie " – 3: 18
# To Lie with Lions ( 1995 )
# it is torsion-free, i. e., for any vector fields X and Y we have, where is the Lie bracket of the vector fields X and Y.
# REDIRECT Lie algebra representation
# REDIRECT Representation of a Lie group
# REDIRECT King Lie of Zhou
# REDIRECT Lie superalgebra
Studying projective representations of Lie groups leads one to consider true representations of their central extensions ( see Group extension # Lie groups ).
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