Category:Lie groups

A

• ► Algebraic groups‎ (3 C, 51 P)

H

• ► Hypergeometric functions‎ (1 C, 30 P)

I

• ► Invariant theory‎ (1 C, 36 P)

L

• ► Lie algebras‎ (2 C, 103 P)

R

• ► Representation theory of Lie groups‎ (1 C, 54 P)
• ► Rotation in three dimensions‎ (2 C, 28 P)
• ► Rotational symmetry‎ (1 C, 53 P)

S

• ► Special functions‎ (8 C, 99 P)

S cont.

• ► Supersymmetry‎ (1 C, 76 P)

T

• ► Topology of Lie groups‎ (1 C, 7 P)

• Glossary of semisimple groups
• List of Lie groups topics

A

• ADE classification
• Adjoint endomorphism
• Affine group
• Ahlfors finiteness theorem
• An Exceptionally Simple Theory of Everything
• Automorphic form

B

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

C

• Carnot group
• 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 element

D

• Darboux derivative
• Dunkl operator

E

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

F

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

G

• G2 (mathematics)
• Gell-Mann matrices
• General linear group
• General semilinear group
• GL(n,C)
• Group algebra

H

• Haar measure
• Harish-Chandra's c-function

H cont.

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

I

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

J

• Jacobi group
• 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 group homomorphism
• Lie point symmetry
• Lie product formula
• Lie subgroup
• Lie theory
• Lie's third theorem
• List of simple Lie groups
• Lorentz group

M

• Matrix exponential
• Maurer–Cartan form
• Maximal compact subgroup
• Maximal torus
• McKay graph
• Möbius transformation
• Mostow–Palais theorem

N

• Nilmanifold

O

• One-parameter group
• Oppenheim conjecture
• Orthogonal group

P

• P-compact group
• Pansu derivative
• Pauli matrices
• Pin group

P cont.

• Ping-pong lemma
• Poincaré group
• Poisson–Lie group
• Pre-Lie algebra
• 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
• Regular element of a Lie algebra
• Representation of a Lie group
• Representation ring
• Root system
• Rotation group SO(3)

S

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

T

• Table of Lie groups
• Theta representation
• Triality
• Trombi–Varadarajan theorem

U

• Unitary group

V

• Vector flow
• Vogel plane

W

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