List Of Lie Group Topics
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List Of Lie Group Topics
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mathematics-related lists
lie groups
lie algebras
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EXAMPLES
''See
Table Of Lie Groups
for a list''
General Linear Group
,
Special Linear Group
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 Poincare 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 ALGEBRA
S
Commutator
Jacobi Identity
Universal Enveloping Algebra
Campbell-Hausdorff Formula
Casimir Invariant
Kac-Moody Algebra
Affine Lie Algebra
Loop Algebra
FOUNDATIONAL RESULTS
One-parameter Group
,
One-parameter Subgroup
Matrix Exponential
Infinitesimal Transformation
Maurer-Cartan Form
Cartan's Theorem
Hausdorff Paradox
Local Lie Group
Formal Group Law
Hilbert's Fifth Problem
Hilbert-Smith Conjecture
Lie Group Decompositions
SEMISIMPLE THEORY
Simple Lie Group
,
Compact Lie Group
Root System
Simply Laced Group
---
ADE Classification
Maximal Torus
Weyl Group
Dynkin Diagram
Coxeter Group
REPRESENTATION THEORY
''See also'':
List Of Harmonic Analysis And Representation Theory Topics
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
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
Lie Groupoid
Lie Algebroid
Discrete Group
s
Lattice (group)
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)
