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Lie groups
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Lie groups
and
Lie algebras
Classical groups
General linear
GL(
n
)
Special linear
SL(
n
)
Orthogonal
O(
n
)
Special orthogonal
SO(
n
)
Unitary
U(
n
)
Special unitary
SU(
n
)
Symplectic
Sp(
n
)
Simple Lie groups
Classical
A
n
B
n
C
n
D
n
Exceptional
G
2
F
4
E
6
E
7
E
8
Other Lie groups
Circle
Lorentz
Poincaré
Conformal group
Diffeomorphism
Loop
Euclidean
Lie algebras
Lie group–Lie algebra correspondence
Exponential map
Adjoint representation
Killing form
Index
Simple Lie algebra
Loop algebra
Affine Lie algebra
Semisimple Lie algebra
Dynkin diagrams
Cartan subalgebra
Root system
Weyl group
Real form
Complexification
Split Lie algebra
Compact Lie algebra
Representation theory
Lie group representation
Lie algebra representation
Representation theory of semisimple Lie algebras
Representations of classical Lie groups
Theorem of the highest weight
Borel–Weil–Bott theorem
Lie groups in
physics
Particle physics and representation theory
Lorentz group representations
Poincaré group representations
Galilean group representations
Scientists
Sophus Lie
Henri Poincaré
Wilhelm Killing
Élie Cartan
Hermann Weyl
Claude Chevalley
Harish-Chandra
Armand Borel
Glossary
Table of Lie groups
v
t
e
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