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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
People
Examples
edit
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 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
G
2
F
4
E
6
E
7
E
8
Affine group
Euclidean group
Poincaré group
Heisenberg group
Lie algebras
edit
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
edit
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
edit
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
edit
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
edit
Physical 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 algebra
Geometry
edit
Erlangen programme
Homogeneous space
Principal homogeneous space
Invariant theory
Lie derivative
Darboux derivative
Lie groupoid
Lie algebroid
Discrete 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 form
Algebraic groups
edit
Borel subgroup
Arithmetic group
Special functions
edit
Dunkl operator
Automorphic forms
edit
Modular form
Langlands program
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)
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https://en.wikipedia.org/w/index.php?title=List_of_Lie_groups_topics&oldid=1194796773
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