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独裁统治 China Dictatorship 新疆改造中心、六四事件、法轮功、郝海东、709大抓捕、2015巴拿马文件 邓家贵、低端人口、西藏骚乱
Important Lie group
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Mathematics
Area of mathematics
Geometry
Differential geometry
Lie group
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words: 3k
articles: 67
Table of contents
3k
67
Matrix Lie group
Important Lie group
284
4
Every closed subgroup of
G
L
(
n
,
C
)
is a Lie group
Matrix Lie group
2
Lie algebra of a matrix Lie group
Matrix Lie group
273
2
Lie bracket of a matrix Lie group
Lie algebra of a matrix Lie group
69
One parameter subgroup
Lie algebra of a matrix Lie group
73
Classical group
Important Lie group
141
3
Symplectic group
(
S
p
(
n
,
F
)
)
Classical group
141
2
Symplectic matrix
Symplectic group
Unitary symplectic group
(
S
p
(
n
)
)
Symplectic group
General linear group
(
G
L
(
n
)
,
G
L
(
n
,
F
)
)
Important Lie group
102
1
Finite general linear group
(
G
L
(
n
,
F
m
)
,
G
L
(
n
,
m
)
)
General linear group
45
Lie algebra of
G
L
(
n
)
Important Lie group
47
Special linear group
(
S
L
(
n
)
)
Important Lie group
534
4
Special linear group of dimension 2
(
S
L
(
2
)
)
Special linear group
Lie algebra of
S
L
(
n
)
Special linear group
486
1
Lie algebra of
S
L
(
2
)
Lie algebra of
S
L
(
n
)
486
Finite special general linear group
(
S
L
(
n
,
m
)
)
Special linear group
37
Isometry group
Important Lie group
102
1
Lie algebra of a isometry group
Isometry group
86
Orthogonal group
(
O
(
n
)
)
Important Lie group
855
23
Definition of the orthogonal group
Orthogonal group
281
5
The orthogonal group is the group of all matrices that preserve the dot product
Definition of the orthogonal group
160
1
What happens to the definition of the orthogonal group if we choose other types of symmetric bilinear forms
The orthogonal group is the group of all matrices that preserve the dot product
104
The orthogonal group is the group of all invertible matrices where the inverse is equal to the transpose
Definition of the orthogonal group
82
1
Elements of the orthogonal group have determinant plus or minus one
The orthogonal group is the group of all invertible matrices where the inverse is equal to the transpose
The orthogonal group is the group of all matrices with orthonormal rows and orthonormal columns
Definition of the orthogonal group
23
Topology of the orthogonal group
Orthogonal group
257
2
The orthogonal group is compact
Topology of the orthogonal group
Connected components of the orthogonal group
(The orthogonal group has two connected components)
Topology of the orthogonal group
257
Lie algebra of
O
(
n
)
Orthogonal group
3
Special orthogonal group
(
S
O
(
n
)
, Rotation group)
Orthogonal group
206
3
Lie algebra of
S
O
(
3
)
Special orthogonal group
171
1
Lie bracket of the rotation group
Lie algebra of
S
O
(
3
)
16
3D rotation group
(
S
O
(
3
)
)
Special orthogonal group
4
Unitary group
(
U
(
n
)
)
Orthogonal group
108
8
Unitary group of degree 1
(
U
(
1
)
)
Unitary group
Unitary group of degree 2
(
U
(
2
)
)
Unitary group
5
Unit circle
Unitary group
12
Special unitary group
(
S
U
(
n
)
)
Unitary group
44
4
Special unitary of degree 2
(
S
U
(
2
)
)
Special unitary group
9
3
Representations of
S
U
(
2
)
Special unitary of degree 2
4
2
Lie algebra of
S
U
(
2
)
Representations of
S
U
(
2
)
3
2D representation of
S
U
(
2
)
Representations of
S
U
(
2
)
1
Projective linear group
Important Lie group
20
5
Finite projective linear group
(
P
G
L
(
q
,
p
)
)
Projective linear group
Projective special linear group
Projective linear group
8
3
Finite projective special linear group
(
P
S
L
(
p
,
q
)
)
Projective special linear group
8
2
P
S
L
(
2
,
p
)
Finite projective special linear group
8
1
PSL(2,7)
P
S
L
(
2
,
p
)
8
Poincaré group
Important Lie group
1k
17
Galilean transformation
Poincaré group
460
6
Translation
(geometry)
Galilean transformation
139
2
Translation group
Translation
133
1
The derivative is the generator of the translation group
Translation group
121
Galilean invariance
Galilean transformation
321
2
Covariance
Galilean invariance
133
1
Invariant vs covariant
Covariance
43
Lorentz group
(
S
O
(
1
,
3
)
)
Poincaré group
552
9
Representation theory of the Lorentz group
Lorentz group
72
3
Representation of the Lorentz group
Representation theory of the Lorentz group
20
2
Lie algebra of the Lorentz group
Representation of the Lorentz group
Spinor
Representation of the Lorentz group
8
Lorentz boost
Lorentz group
40
Indefinite orthogonal group
(
O
(
m
,
n
)
)
Lorentz group
293
3
Definition of the indefinite orthogonal group
Indefinite orthogonal group
267
1
All indefinite orthogonal groups of matrices of equal metric signature are isomorphic
Definition of the indefinite orthogonal group
135
Indefinite special orthogonal group
(
S
O
(
m
,
n
)
)
Indefinite orthogonal group
15
Ancestors
(6)
Lie group
Differential geometry
Geometry
Area of mathematics
Mathematics
Home
Synonyms
(1)
Important Lie groups
Ciro Santilli
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