Category:Lie groups

A

• [+] Algebraic groups (3)

H

• [+] Hypergeometric functions (1)

I

• [+] Invariant theory (1)

L

• [+] Lie algebras (1)

R

• [+] Representation theory of Lie groups (1)
• [+] Rotational symmetry (1)

S

• [+] Special functions (9)
• [+] Supersymmetry (1)

T

• [+] Topology of Lie groups (1)

• List of Lie group topics
• Glossary of semisimple groups

A

• ADE classification
• Adjoint endomorphism
• Affine group
• An Exceptionally Simple Theory of Everything
• Analytic subgroup
• Automorphic form

B

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

C

• Cartan decomposition
• Cartan subgroup
• Cartan's theorem
• Charts on SO(3)
• Chevalley basis
• Circle group
• Classical group
• Clifford-Klein form
• Compact group
• Complex reflection group
• Continuous symmetry
• Covering group
• Coxeter number

D

• Darboux derivative
• Dunkl operator

E

• E6 (mathematics)
• E7 (mathematics)
• E7½
• E8 (mathematics)
• En (Lie algebra)
• Euclidean group
• Exponential map

F

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

G

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

G cont.

• Group algebra

H

• Haar measure
• Heisenberg group
• Hermitian symmetric space
• Hilbert's fifth problem
• 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
• Lie group decomposition
• Lie product formula
• Lie subgroup
• Lie theory
• Lie's third theorem
• List of simple Lie groups
• Longest element of a Coxeter group
• Lorentz group

M

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

N

• Nilmanifold
• Nilpotent Lie algebra

O

• One-parameter group
• Oppenheim conjecture
• Orthogonal group

P

• P-compact group

P cont.

• Pauli matrices
• Pin group
• Ping-pong lemma
• Poincaré group
• Poisson–Lie group
• Principal homogeneous space
• Projective linear 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
• Rotation group

S

• SL2(R)
• SO(4)
• SO(5)
• SO(8)
• Schottky group
• Segal-Shale-Weil distribution
• Simple Lie group
• Solvable Lie algebra
• Special affine group
• Special linear group
• Special unitary group
• Spin group
• Symmetric space
• Symplectic group

T

• Table of Lie groups
• Theta representation
• Triality

U

• Unitary group

V

• Vector flow

W

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