# 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 ( disambiguation )

# 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 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 ).

65 # 4 ( Autumn, 1991 ), pp. 1 – 12 in JSTOR

2 # 1 ( Jan., 1940 ), pp. 87 – 104 in JSTOR

* 1961 – Motown releases what would be its first # 1 hit, " Please Mr. Postman " by The Marvelettes.

# Maria Komnene, who married ( 1 ) Gregory Gabras and ( 2 ) Nikephoros Katakalon.

# Theodora Komnene, who married ( 1 ) Constantine Kourtikes and ( 2 ) Constantine Angelos.

# 1. around 1200: Gertrude of Merania ( 1185 – 8 September 1213 ), a daughter of Berthold IV, Duke of Merania and his wife, Agnes of Wettin

ASU Online was ranked # 1 in online Student Services and Technology by U. S. News and World Report.

# An aircraft should be “ in flight ” ( that is, according to Article 1, paragraph 3 of the Tokyo Convention, from the moment when power is applied for the purpose of take-off until the moment when the landing run ends );

( Slot # 1 to the front of the interface took priority if both were populated ).

# Abijah ( queen ), the daughter of Zechariah ( 2 Chronicles 29: 1 ), who married King Ahaz of Judah.

# A descendant of Eleazar, the son of Aaron, a chief of one of the twenty-four orders into which the priesthood was divided by David ( 1 Chr.

The original meaning may have been # 1, and Ζευς ' Αιγιοχος =

* Programming In Atlas Autocode-Edinburgh University Computer Unit Report # 1 ( 1965 ).

Between 1980-1985 a few Dutch Hip Hop records had already been released, but in 1986 Dutch rap duo MC Miker G & DJ Sven ( Lucien Witteveen and Sven van Veen ) had a major top 10 hit ( often # 1 ) across Europe with their " Holiday Rap ", which sampled Madonna's " Holiday ".

In the mid 2000s Cilvaringz, Ali B and Raymzter have commercially been successful and Lange Frans & Baas B have had multiple # 1 hits.

* Rhythm conga # 1

* C Information Bulletin # 1 ( ANSI X3J11 / 93-007 ) ( May 27, 1992 )

* Set Theory, Skolem's Paradox and the Tractatus, A. W. Moore, Analysis 45, # 1 ( January 1985 ), pp. 13 – 20.

# Albert Frederick of Prussia ( 1 June – 8 October 1580 ).

Flatt and Scruggs subsequently cut their own version of the theme ( with Flatt singing ) for Columbia Records ; released as a single, it reached # 44 on Billboard Hot 100 pop music chart and # 1 on the Billboard Hot Country chart ( the lone country chart-topper for the duo ).

# REDIRECT BBC Radio 1

The group achieved great success globally and scored a chain of # 1 hits.

The Paige / Dickson duet " I Know Him So Well " became a major UK # 1 hit, and Murray Head's " One Night in Bangkok " gave Andersson / Ulvaeus a US # 3 hit.