List of Lie group topics
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This is a list of Lie group topics, by Wikipedia page.
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Examples
See Table of Lie groups for a list
- General linear group, special linear group
- Unitary group, special unitary group
- Orthogonal group, special orthogonal group
- Symplectic group
- Exceptional groups
- Affine group
- Euclidean group
- Poincaré group
- Heisenberg group
Lie algebras
- 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
- Maximal torus
- Weyl group
- Dynkin diagram
- Coxeter group
Representation theory
See also: List of harmonic analysis and representation theory topics
- Representations of Lie groups
- Representation of Lie algebras
- Adjoint representation
- Unitary representation
- Weight
- Peter-Weyl theorem
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
Discrete groups
- 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 groups
Special functions
Automorphic forms
People
- Sophus Lie (1842 – 1899)
- Wilhelm Killing (1847 – 1923)
- Élie Cartan (1869 – 1951)
- Hermann Weyl (1885 – 1955)