Lie groups and Lie algebra

 

 

 

Sophus Lie Wilhelm Killing Elie Cartan Hermann Weyl

  1. Introduction  [Prove that] O(n) is a Lie group   [SO(2) SO(3)] [SU(2)]
  2. Basic results on Lie groups  [Hyperbolic planes]
  3. Lie group with bi-invariant metric
    [Prove that ]Lie algebra isomorphism to left-inavriant fields
  4. Proper and isometric actions
  5. Adjiont and conjugate actions
  6. Singular Tiemannian foliations with sections
  7. Applications in physics
  8. Lie groups and DE   Iwasawa decomposition theorem   Galois dream   [E8 Lie group]

參考書目

  1. Introduction to Lie groups and Lie algebras      ResearchGateR  Alexander Kirillov JR
  2. Lectures on Lie Groups 項武義
  3. Lie Groups New Research      Altos B. Canterra
  4. Structure and Geometry of Lie Groups    Joachim Hilgert and Karl-Hermann Need
  5. Foundations of Differentiable Geometry and Lie Groups   Frank W. Warner
  6. Lie Algebras for Physicists     Douglas W. McKenzie
  7. Lie Groups Differential Equation and Geometry   Giovanni Falcone