Index Concordia

Groups

[UNDER CONSTRUCTION!]

Here you can find a very bad version of my notes from professor van Nieuwenhuizen’s course on group theory during the fall of 2007.

  • Week 01 – Introduction
  • Week 02 – Finite groups
  • Week 03 – More finite groups
  • Week 04 – The Dirac group, faithful representations, Schur lemmas, Dirac matrices in different dimensions, charge conjugation matrices, Majorana representations
  • Week 05 – More on the Dirac group, characters, application to vibrational modes of molecules, polyhedra
  • Week 06 – Historical overview of Lie groups and algebras, definitions, PoincarĂ© algebra, SU(2) vs. SO(3), covering groups
  • Week 07 – Lorentz group and SL(2, \mathbb{C}), group manifolds, Lie bracket, real and complex algebras, List of groups and homomorphisms
  • Week 08 -Sub-algebras, simple and semi-simple algebras, A_{n}, B_{n}, C_{n}, D_{n} series, and their algebras and groups, defining representations, real forms
  • Week 09 – Roots and weights for so(2N) algebra
  • Week 10 – Positive roots, simple roots, Dynkin diagrams, Killing metric; roots, weights and generators for su(N) algebra, fundamental weights, tensor products of irreducible representations
  • Week 11 –
  • Week 12 –
  • Week 13 –
  • Week 14 –
  • Week 14 –
  • Week 15 –
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