| course |
dates |
credits |
| Group Theory |
Oct 2 - Oct 26 |
3 |
| teachers |
schedule |
term |
|
|
10:00 - 11:15 |
1 |
Program:
Topology
Differentiable manifolds: vector fields, forms, integration, Lie derivative
Lie groups: action of groups on manifolds, Lie algebras
Fibre bundles: connections, curvature, covariant derivative
Lie algebras: simple and semi-simple algebras, Killing form,
Cartan-Weyl basis, weights, Cartan matrix and Dynkin diagrams,
classification of simple Lie algebras, Weyl group, congruence classes,
low-rank examples
Highest-weight representations: Dynkin labels, Freudenthal
multiplicity formula, Casimir operators, Dynkin index, tensor product
decomposition, su(N) and Young diagrams
Real forms and compact Lie groups: split and compact real form
Spinors in various dimensions
Prerequisites:
Books:
Online Resources:
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