List of Lie groups topics

December 18, 2023

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

Examples edit

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 edit

Foundational results edit

Semisimple theory edit

Representation theory edit

Applications edit

Special functions edit

Dunkl operator

Automorphic forms edit

People edit

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)

December 18, 2023

list, groups, topics, this, list, group, topics, wikipedia, page, contents, examples, algebras, foundational, results, semisimple, theory, representation, theory, applications, physical, theories, geometry, discrete, groups, algebraic, groups, special, functio. This is a list of Lie group topics by Wikipedia page Contents 1 Examples 2 Lie algebras 3 Foundational results 4 Semisimple theory 5 Representation theory 6 Applications 6 1 Physical theories 6 2 Geometry 6 3 Discrete groups 6 4 Algebraic groups 7 Special functions 7 1 Automorphic forms 8 PeopleExamples editSee 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 Poincare disk model of the Hyperbolic plane Lorentz group Spinor group Symplectic group Exceptional groups G2 F4 E6 E7 E8 Affine group Euclidean group Poincare group Heisenberg groupLie algebras editCommutator Jacobi identity Universal enveloping algebra Baker Campbell Hausdorff formula Casimir invariant Killing form Kac Moody algebra Affine Lie algebra Loop algebra Graded Lie algebraFoundational results editOne 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 editSimple 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 formulaRepresentation theory editSee 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 editPhysical theories edit 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 algebraGeometry edit Erlangen programme Homogeneous space Principal homogeneous space Invariant theory Lie derivative Darboux derivative Lie groupoid Lie algebroidDiscrete groups edit 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 formAlgebraic groups edit Borel subgroup Parabolic subgroup Arithmetic groupSpecial functions editDunkl operatorAutomorphic forms edit Modular form Langlands programPeople editSophus Lie 1842 1899 Wilhelm Killing 1847 1923 Elie Cartan 1869 1951 Hermann Weyl 1885 1955 Harish Chandra 1923 1983 Lajos Pukanszky 1928 1996 Bertram Kostant 1928 2017 Retrieved from https en wikipedia org w index php title List of Lie groups topics amp oldid 1182627258, wikipedia, wiki, book, books, library,

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