List of Lie groups topics

This is a list of Lie group topics, by Wikipedia page.

Examples
See Table of Lie groups for a list


 * General linear group, special linear group
 * SL2(R)
 * SL2(C)
 * Unitary group, special unitary group
 * SU(2)
 * SU(3)
 * Orthogonal group, special orthogonal group
 * Rotation group SO(3)
 * SO(8)
 * Generalized orthogonal group, generalized special orthogonal group
 * The special unitary group SU(1,1) is the unit sphere in the ring of coquaternions. It is the group of hyperbolic motions of the Poincaré disk model of the Hyperbolic plane.
 * Lorentz group
 * Spinor group
 * Symplectic group
 * Exceptional groups
 * G2
 * F4
 * E6
 * E7
 * E8
 * Affine group
 * Euclidean group
 * Poincaré group
 * Heisenberg group

Lie algebras

 * Commutator
 * Jacobi identity
 * Universal enveloping algebra
 * Baker-Campbell-Hausdorff formula
 * Casimir invariant
 * Killing form
 * Kac–Moody algebra
 * Affine Lie algebra
 * Loop algebra
 * Graded Lie algebra

Foundational results

 * One-parameter group, One-parameter subgroup
 * Matrix exponential
 * Infinitesimal transformation
 * Lie's third theorem
 * Maurer–Cartan form
 * Cartan's theorem
 * Cartan's criterion
 * Local Lie group
 * Formal group law
 * Hilbert's fifth problem
 * Hilbert-Smith conjecture
 * Lie group decompositions
 * Real form (Lie theory)
 * Complex Lie group
 * Complexification (Lie group)

Semisimple theory

 * Simple Lie group
 * Compact Lie group, Compact real form
 * Semisimple Lie algebra
 * Root system
 * Simply laced group
 * ADE classification
 * Maximal torus
 * Weyl group
 * Dynkin diagram
 * Weyl character formula

Representation theory

 * Representation of a Lie group
 * Representation of a Lie algebra
 * Adjoint representation of a Lie group
 * Adjoint representation of a Lie algebra
 * Unitary representation
 * Weight (representation theory)
 * Peter–Weyl theorem
 * Borel–Weil theorem
 * Kirillov character formula
 * Representation theory of SU(2)
 * Representation theory of SL2(R)

Physical theories

 * Pauli matrices
 * Gell-Mann matrices
 * Poisson bracket
 * Noether's theorem
 * Wigner's classification
 * Gauge theory
 * Grand unification theory
 * Supergroup
 * Lie superalgebra
 * Twistor theory
 * Anyon
 * Witt algebra
 * Virasoro algebra

Geometry

 * Erlangen programme
 * Homogeneous space
 * Principal homogeneous space
 * Invariant theory
 * Lie derivative
 * Darboux derivative
 * Lie groupoid
 * Lie algebroid

Discrete groups

 * Lattice (group)
 * Lattice (discrete subgroup)
 * Frieze group
 * Wallpaper group
 * Space group
 * Crystallographic group
 * Fuchsian group
 * Modular group
 * Congruence subgroup
 * Kleinian group
 * Discrete Heisenberg group
 * Clifford–Klein form

Algebraic groups

 * Borel subgroup
 * Arithmetic group

Special functions

 * Dunkl operator

Automorphic forms

 * Modular form
 * Langlands program

People

 * Sophus Lie (1842 – 1899)
 * Wilhelm Killing (1847 – 1923)
 * Élie Cartan (1869 – 1951)
 * Hermann Weyl (1885 – 1955)
 * Harish-Chandra (1923 – 1983)
 * Lajos Pukánszky (1928 – 1996)
 * Bertram Kostant (1928 – 2017)