Editing List of Lie groups topics

{{Short description|none}}
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)|SL<sub>2</sub>('''R''')]]
**[[SL2(C)|SL<sub>2</sub>('''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 [[coquaternion]]s. It is the group of [[hyperbolic motion]]s of the Poincaré disk model of the [[Hyperbolic geometry|Hyperbolic plane]].
***[[Lorentz group]]
**[[Spinor group]]
*[[Symplectic group]]
*Exceptional groups
**[[G2 (mathematics)|G<sub>2</sub>]]
**[[F4 (mathematics)|F<sub>4</sub>]]
**[[E6 (mathematics)|E<sub>6</sub>]]
**[[E7 (mathematics)|E<sub>7</sub>]]
**[[E8 (mathematics)|E<sub>8</sub>]]
*[[Affine group]]
*[[Euclidean group]]
*[[Poincaré group]]
*[[Heisenberg group]]

==[[Lie algebra]]s==

*[[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]]
*[[Closed subgroup theorem|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==
{{see also|List of representation theory topics}}

*[[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)]]

==Applications==

===Physical theories===
*[[Pauli matrices]]
*[[Gell-Mann matrices]]
*[[Poisson bracket]]
*[[Noether's theorem]]
*[[Wigner's classification]]
*[[Gauge theory]]
*[[Grand unification theory]]
*[[Supergroup (physics)|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 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]]
*[[Arithmetic group]]

==[[Special functions]]==

*[[Dunkl operator]]

===Automorphic forms===
*[[Modular form]]
*[[Langlands program]]

==People==

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

[[Category:Mathematics-related lists|Lie groups]]
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[[Category:Outlines|Lie groups]]