Groups « 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, Poincaré 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 -