Category:Lie groups

A

• ► Algebraic groups‎ (3 C, 35 P)

I

• ► Invariant theory‎ (1 C, 20 P)

L

• ► Lie algebras‎ (2 C, 63 P)

R

• ► Representation theory of Lie groups‎ (1 C, 39 P)
• ► Rotational symmetry‎ (1 C, 46 P)

S

• ► Special functions‎ (4 C, 73 P)
• ► Supersymmetry‎ (1 C, 64 P)

T

• ► Topology of Lie groups‎ (1 C, 5 P)

• Glossary of semisimple groups
• Lie theory
• List of Lie groups topics

A

• ADE classification
• Adjoint representation of a Lie algebra
• Affine group
• Automorphic form

B

• Baker–Campbell–Hausdorff formula
• Bianchi classification
• Bruhat decomposition

C

• Cartan decomposition
• Cartan subgroup
• Cartan's theorem
• Circle group
• Clifford–Klein form
• Compact group
• Complex Lie group
• Continuous symmetry
• Covering group
• Coxeter element

D

• Dunkl operator

E

• E6 (mathematics)
• E7 (mathematics)
• E8 (mathematics)
• Euclidean group
• An Exceptionally Simple Theory of Everything

F

• F4 (mathematics)
• Freudenthal magic square
• Fundamental representation
• Fundamental vector field

G

• G2 (mathematics)
• Gell-Mann matrices
• General linear group
• General semilinear group

H

• Haar measure
• Hermitian symmetric space
• Hilbert's fifth problem
• Homogeneous space

I

• Identity component
• Improper rotation
• Indefinite orthogonal group
• Infinitesimal transformation
• Irrational winding of a torus
• Iwasawa decomposition

J

• Jet group

K

• Killing form
• Klein geometry
• Kleinian group

L

• Langlands decomposition
• Lattice (discrete subgroup)
• Lattice (group)
• Lie algebra
• Lie algebra extension
• Lie group
• Lie point symmetry
• Lorentz group

M

• Matrix exponential
• Maurer–Cartan form
• Maximal compact subgroup
• Maximal torus
• Möbius transformation

N

• Nilmanifold

O

• One-parameter group
• Oppenheim conjecture
• Orthogonal group

P

• P-compact group
• Pauli matrices
• Pin group
• Ping-pong lemma
• Poincaré group
• Poisson–Lie group
• Polar decomposition
• Principal homogeneous space
• Projective linear group
• Projective orthogonal group
• Projective semilinear group
• Projective unitary group
• Pseudogroup

R

• Ratner's theorems
• Reductive group
• Representation of a Lie group
• Representation ring
• Root system
• Rotation group SO(3)

S

• Simple Lie group
• SL2(R)
• SO(5)
• SO(8)
• Special affine group
• Special linear group
• Special unitary group
• Spin tensor
• Symmetric cone
• Symmetric space
• Symplectic group

T

• Table of Lie groups
• Theta representation
• Triality

U

• Unitary group

V

• Vector flow

W

• Wess–Zumino–Witten model
• Weyl group