Category:Lie groups

A

• Algebraic groups (3 C, 34 P)

H

• Hypergeometric functions (1 C, 26 P)

I

• Invariant theory (1 C, 28 P)

L

• Lie algebras (2 C, 92 P)

R

• Representation theory of Lie groups (1 C, 49 P)
• Rotational symmetry (1 C, 52 P)

S

• Special functions (8 C, 103 P)
• Supersymmetry (1 C, 39 P)

T

• Topology of Lie groups (1 C, 9 P)

• Lie group
• Lie theory
• List of Lie groups topics

3

• 3D rotation group

A

• ADE classification
• Adjoint representation
• Affine group
• Algebraic torus
• Automorphic form

B

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

C

• Cartan decomposition
• Cartan's theorem
• Charts on SO(3)
• Chevalley basis
• Circle group
• Classical group
• Clifford–Klein form
• Compact group
• Complex Lie group
• Continuous symmetry
• Covering group
• Coxeter element

D

• Darboux derivative
• Dunkl operator

E

• E6 (mathematics)
• E7 (mathematics)
• E7½
• E8 (mathematics)
• En (Lie algebra)
• Euclidean group
• An Exceptionally Simple Theory of Everything

F

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

G

• G2 (mathematics)
• General linear group
• General semilinear group
• Group algebra of a locally compact group

H

• Haar measure
• Heisenberg group
• Hermitian symmetric space
• Hilbert's fifth problem
• Hitchin system
• Homogeneous space

I

• Identity component
• Improper rotation
• Indefinite orthogonal group
• Infinitesimal transformation
• Iwasawa decomposition
• Iwasawa manifold

J

• Jet group

K

• Killing form
• Klein geometry
• Kleinian group

L

• Langlands decomposition
• Lattice (discrete subgroup)
• Lattice (group)
• Lie algebra
• Lie group decomposition
• Lie groupoid
• Lie product formula
• Lie's third theorem
• Linear flow on the torus
• Lorentz group

M

• Margulis lemma
• 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

Q

• Quaternion-Kähler symmetric space

R

• Ratner's theorems
• Real form (Lie theory)
• Reductive group
• Representation of a Lie group
• Representation ring
• Root system

S

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

T

• Table of Lie groups
• Theta representation
• Topological group
• Triality

U

• Unitary group

V

• Vector flow

W

• Weakly symmetric space
• Wess–Zumino–Witten model
• Weyl group