List of Lie group topics

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

Table of contents

1 Examples 2 Lie algebras 3 Semisimple theory 4 Lie group decompositions 5 Representation theory 6 Applications 7 History

Examples

• General linear group, special linear group
• Unitary group, special unitary group
• Orthogonal group, special orthogonal group, generalized special orthogonal group
  • Charts on SO(3)
• Symplectic group
• G2 (mathematics)
• F4 (mathematics)
• E6 (mathematics)
• Affine group
• Lorentz group
• Poincaré group

Lie algebras

• Commutator
• Jacobi identity
• Adjoint representation
• Universal enveloping algebra
• Campbell-Hausdorff formula

Semisimple theory

• Simple Lie group
• Root system
• Maximal torus
• Weyl group
• Dynkin diagram
• Coxeter group

Lie group decompositions

Representation theory

• Representation of Lie algebras
• Representations of Lie groups and algebras
• Weight (representation theory)
• Unitary representation
• Peter-Weyl theorem

Applications

• Physical theories
  • Poisson bracket
  • Noether's theorem
  • Wigner's classification
  • SU(3)XSU(2)XU(1)
  • Flipped SU(5)
  • Anti de Sitter space
  • De Sitter space
  • Supergroup (physics)
  • Superalgebra
  • Twistor
  • Anyon
• Geometry
  • Erlangen programme
  • Homogeneous space
    • Principal homogeneous space
  • Invariant theory
  • Lie derivative
  • Lie groupoid
  • Lie algebroid
• Automorphic forms
  • Langlands program

History

• Sophus Lie (1842-1899)