Ciro Santilli
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Important mathematical groups
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⇓ toc
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Table of contents
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1. Important discrete mathematical groups
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4
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11
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1.1. Cyclic group (
Z
n
​
)
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1.2. Alternating group (
A
n
​
)
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1.3. Wallpaper group
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3
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1.4. Space group
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8
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2. Lie group
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187
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17
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815
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2.1. Applications of Lie groups to differential equations
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96
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2.2. Lie algebra
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2.3. Continuous symmetry
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17
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1
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36
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2.3.1. Local symmetry
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19
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2.4. Important Lie groups
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0
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11
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434
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2.4.1. General linear group (
G
L
(
n
)
)
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42
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2.4.2. Special linear group (
S
L
(
n
)
)
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17
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2.4.3. Orthogonal group (
O
(
n
)
)
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154
,
1
,
175
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2.4.3.1. Special orthogonal group (
S
O
(
n
)
)
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21
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2.4.4. Unitary group (
U
(
n
)
)
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77
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3
,
147
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2.4.4.1. Unitary group of dimension 2 (
U
(
2
)
)
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5
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2.4.4.2. Unit circle
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18
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2.4.4.3. Special unitary group (
S
U
(
n
)
)
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47
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2.4.5. Poincare group
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21
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2
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53
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2.4.5.1. Lorentz group (
S
O
(
1
,
3
)
)
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15
,
1
,
32
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↑ parent "Poincare group"
2.4.5.1.1. Indefinite orthogonal group (
S
O
(
m
,
n
)
)
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17
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↑ parent "Lorentz group"
2.5. Representation theory
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62
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