Syllabus: Introductory Algebra for Physicists, 2016/17

• Finite groups. Subgroups and classes. Coset decomposition.
  
  
• Invariant subgroups and quotient groups.
  
  
• Groups of permutations.
  
  
• Representations of finite groups. Characters. Irreducible representations.
  
  
• Kronecker product and Clebsch-Gordan series. Wigner-Eckart theorem.
  
  
• Continuous groups. Lie algebras. Killing form.
  
  
• Cartan subalgebra. Roots.
  
  
• Cartan-Weyl basis, simple roots and Cartan matrix. Dynkin diagrams.
  
  
• Representations of Lie algebras.