Lie groups

A

• Algebraic groups (5 C, 68 P)

E

• Exceptional Lie algebras (7 P)

H

• Hypergeometric functions (1 C, 34 P)

I

• Invariant theory (1 C, 57 P)

L

• Lie algebras (3 C, 143 P)

R

• Representation theory of Lie groups (1 C, 62 P)
• Rotation in three dimensions (2 C, 32 P)
• Rotational symmetry (53 P)

S

• Special functions (8 C, 152 P)
• Supersymmetry (1 C, 48 P)

T

• Topology of Lie groups (1 C, 9 P)

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

2

• 2E6 (mathematics)

3

• 3D rotation group
• 3D4

A

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

B

• Baker–Campbell–Hausdorff formula
• Berry–Robbins problem
• Astronomy:Bianchi classification
• Borel–de Siebenthal theory
• Bruhat decomposition

C

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

D

• Darboux derivative
• Derivative of the exponential map
• Dunkl operator

E

• E6 (mathematics)
• E7 (mathematics)
• E7½
• E8 (mathematics)
• Einstein group
• En (Lie algebra)
• Euclidean group
• Exceptional isomorphisms of classical groups
• Physics:An Exceptionally Simple Theory of Everything
• Exponential map (Lie theory)

F

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

G

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

H

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

I

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

J

• Jacobi group
• Jet group

K

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

L

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

M

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

N

• Nilmanifold
• No small subgroup

O

• One-parameter group
• Oppenheim conjecture
• Orthogonal group

P

• P-compact group
• Pansu derivative
• Pauli matrices
• Pin group
• Ping-pong lemma
• Physics:Poincaré group
• Poincaré group
• Poisson–Lie group
• Polar decomposition
• Pre-Lie algebra
• Principal homogeneous space
• Principal orbit type theorem
• 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
• Representations of classical Lie groups
• Root system

S

• Physics:Schrödinger group
• Simple Lie group
• SO(5)
• Special affine group
• Special linear group
• Special linear Lie algebra
• Special unitary group
• Spin group
• Spin tensor
• Spinc group
• Symmetric cone
• Symmetric space
• Symplectic group

T

• Table of Lie groups
• Theta representation
• Topological group

U

• Unitary group

V

• Vector flow
• Virasoro group

W

• Wess–Zumino–Witten model
• Weyl group