Lie Algebra

• Definition, Deviation, Adjoint
• Ideal, Homomorphism
• Jordan Decomposition
• Nilpotent, Solvable, Engel's theorem, Lie theorem
• Trace form, Killing form, Cartan criterion
• semisimple Lie algebra
• Weyl theorem

• Modules and Representation
• Root system
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• Examples
  • Low-dimensional Lie algebra
  • Classical Lie algebra
  • Heisenberg algebra
  • sl(2,C)
    • Representation: Symmetric polynomials, S^m(V)

Linear Algebraic Group

Particle Physics and Lie algebra

Poisson algebra

Reference books