List of Lie groups topics

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

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

• 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

• 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)

• 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 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)

• 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

• Erlangen programme
• Homogeneous space
  • Principal homogeneous space
• Invariant theory
• Lie derivative
• Darboux derivative
• Lie groupoid
• Lie algebroid

• 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

• Borel subgroup
• Parabolic subgroup
• Arithmetic group

• Dunkl operator

• Modular form
• Langlands program

• 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)

This article does not cite any external source. HandWiki requires at least one external source. See citing external sources. Please help improve this article. Unsourced material may be removed in future. Find sources: "List of Lie groups topics" – news · newspapers · books · scholar · JSTOR (2021) (Learn how and when to remove this template message)

0.00 (0 votes) Original source: https://en.wikipedia.org/wiki/List of Lie groups topics. Read more