Category:Lie groups

A

• ► Algebraic groups‎ (5 C, 70 P)

E

• ► Exceptional Lie algebras‎ (7 P)

H

• ► Hypergeometric functions‎ (1 C, 33 P)

I

• ► Invariant theory‎ (1 C, 59 P)

L

• ► Lie algebras‎ (3 C, 156 P)

R

• ► Representation theory of Lie groups‎ (1 C, 60 P)
• ► Rotation in three dimensions‎ (2 C, 29 P)
• ► Rotational symmetry‎ (59 P)

S

• ► Special functions‎ (8 C, 136 P)
• ► Supersymmetry‎ (1 C, 86 P)

T

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

• Glossary of semisimple groups (computing)
• Lie group (computing)
• Lie theory (computing)
• List of Lie groups topics (computing)

2

• 2E6 (mathematics) (computing)

3

• 3D4 (computing)

A

• Abelian Lie group (computing)
• ADE classification (computing)
• Adjoint representation (computing)
• Affine group (computing)
• Ahlfors finiteness theorem (computing)
• Algebraic representation (computing)
• Algebraic torus (computing)
• Automorphic form (computing)

B

• Baker–Campbell–Hausdorff formula (computing)
• Berry–Robbins problem (computing)
• Bianchi classification (computing)
• Borel–de Siebenthal theory (computing)
• Bruhat decomposition (computing)

C

• Carnot group (computing)
• Cartan decomposition (computing)
• Cartan subgroup (computing)
• Cartan's theorem (computing)
• Charts on SO(3) (computing)
• Chevalley basis (computing)
• Chevalley restriction theorem (computing)
• Circle group (computing)
• Classical group (computing)
• Clifford–Klein form (computing)
• Closed-subgroup theorem (computing)
• Compact group (computing)
• Complex Lie group (computing)
• Complex reflection group (computing)
• Complexification (Lie group) (computing)
• Continuous symmetry (computing)
• Covering group (computing)
• Coxeter element (computing)

D

• Darboux derivative (computing)
• Derivative of the exponential map (computing)
• Dunkl operator (computing)

E

• E6 (mathematics) (computing)
• E7 (mathematics) (computing)
• E7½ (computing)
• E8 (mathematics) (computing)
• Einstein group (computing)
• En (Lie algebra) (computing)
• Euclidean group (computing)
• An Exceptionally Simple Theory of Everything (physics)
• Exponential map (Lie theory) (computing)

F

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

G

• G2 (mathematics) (computing)
• General linear group (computing)
• General semilinear group (computing)
• GL(n,C) (computing)
• Group algebra (computing)
• Group algebra of a locally compact group (computing)
• Group contraction (computing)

H

• Haar measure (computing)
• Harish-Chandra's c-function (computing)
• Heisenberg group (computing)
• Hermitian symmetric space (computing)
• Hilbert's fifth problem (computing)
• Hitchin system (computing)
• Homogeneous space (computing)

I

• Identity component (computing)
• Improper rotation (computing)
• Indefinite orthogonal group (computing)
• Infinitesimal transformation (computing)
• Invariant convex cone (computing)
• Iwasawa decomposition (computing)
• Iwasawa manifold (computing)

J

• Jacobi group (computing)
• Jet group (computing)

K

• Kazhdan–Margulis theorem (computing)
• Killing form (computing)
• Klein geometry (computing)
• Kleinian group (computing)
• Kostant's convexity theorem (computing)

L

• Laguerre transformations (computing)
• Langlands decomposition (computing)
• Lattice (discrete subgroup) (computing)
• Lattice (group) (computing)
• Length of a Weyl group element (computing)
• Lie algebra (computing)
• Lie algebra extension (physics)
• Lie group decomposition (computing)
• Lie group–Lie algebra correspondence (computing)
• Lie point symmetry (computing)
• Lie product formula (computing)
• Lie's third theorem (computing)
• Linear flow on the torus (computing)
• List of simple Lie groups (computing)
• Lorentz group (computing)

M

• Margulis lemma (computing)
• Matrix exponential (computing)
• Maurer–Cartan form (computing)
• Maximal compact subgroup (computing)
• Maximal torus (computing)
• Möbius transformation (computing)
• Mostow–Palais theorem (computing)
• Mutation (Jordan algebra) (computing)

N

• Nilmanifold (computing)

O

• One-parameter group (computing)
• Oppenheim conjecture (computing)
• Orthogonal group (computing)

P

• P-compact group (computing)
• Pansu derivative (computing)
• Pauli matrices (computing)
• Pin group (computing)
• Ping-pong lemma (computing)
• Poincaré group (physics)
• Poisson–Lie group (computing)
• Polar decomposition (computing)
• Pre-Lie algebra (computing)
• Principal homogeneous space (computing)
• Principal orbit type theorem (computing)
• Projective linear group (computing)
• Projective orthogonal group (computing)
• Projective semilinear group (computing)
• Projective unitary group (computing)
• Pseudogroup (computing)

Q

• Quaternion-Kähler symmetric space (computing)

R

• Ratner's theorems (computing)
• Real form (Lie theory) (computing)
• Reductive group (computing)
• Regular element of a Lie algebra (computing)
• Representation of a Lie group (computing)
• Representation ring (computing)
• Restricted root system (computing)
• Root system (computing)
• 3D rotation group (computing)

S

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

T

• Table of Lie groups (computing)
• Tangent Lie group (computing)
• Theory of Lie groups (computing)
• Theta representation (computing)
• Topological group (computing)
• Triality (computing)
• Trombi–Varadarajan theorem (computing)

U

• Unitary group (computing)

V

• Vector flow (computing)
• Virasoro group (computing)
• Vogel plane (computing)

W

• Weakly symmetric space (computing)
• Wess–Zumino–Witten model (physics)
• Weyl group (computing)