- List of Lie group topics
This is a

**list of**, by Wikipedia page.Lie group topics**Examples**"See

Table of Lie groups for a list"*

General linear group ,special linear group

**SL_{2}(**R**)

**SL_{2}(**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 ofcoquaternion s. It is the group ofhyperbolic motion s of the Poincaré disk model of thehyperbolic plane .

***Lorentz group

**Spinor group

*Symplectic group

*Exceptional groups

**G_{2}

**F_{4}

**E_{6}

**E_{7}

**E_{8}

*Affine group

*Euclidean group

*Poincaré group

*Heisenberg group Lie algebra s*

Commutator

*Jacobi identity

*Universal enveloping algebra

*Campbell-Hausdorff formula

*Casimir invariant

*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

*Hausdorff paradox

*Local Lie group

*Formal group law

*Hilbert's fifth problem

*Hilbert-Smith conjecture

*Lie group decompositions **emisimple theory***

Simple Lie group ,compact Lie group

*Root system

*Simply laced group

**ADE classification

*Maximal torus

*Weyl group

*Dynkin diagram

*Coxeter group **Representation theory***

Representation of a Lie group

*Representation of a Lie algebra

*Adjoint representation

*Adjoint representation of a Lie algebra

*Unitary representation

*Weight

*Peter-Weyl theorem

*Kirillov character formula

*Representation theory of SU(2)

*Representation theory of SL2(R) **Applications****Physical theories***

Pauli matrices

*Gell-Mann matrices

*Poisson bracket

*Noether's theorem

*Wigner's classification

*Gauge theory

*Grand unification theory

*Supergroup

*Lie superalgebra

*Twistor

*Anyon

*Witt algebra

*Virasoro algebra **Geometry***

Erlangen programme

*Homogeneous space

**Principal homogeneous space

*Invariant theory

*Lie derivative

*Darboux derivative

*Lie groupoid

*Lie algebroid Discrete group s*

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 group s*

Borel subgroup

*Parabolic 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)

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2010.*

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