List of Lie groups topics
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
- Unitary group, special unitary group
- 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
- Affine group
- Euclidean group
- Poincaré group
- Heisenberg group
Lie algebras
Foundational results
- 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
Representation theory
- 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
Geometry
Discrete groups
Algebraic groups
Special functions
Automorphic forms
People
- 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
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