|00||Properties of Groups, Conjugay Classes, Normal Subgroups
|01||Isomorphism Theorems, Quotient- and Product Groups
Note: Changed the definition of the semidirect product to match that of the lecture.
Addendum to H1.2(d)
|02||Group Actions, Properties of Groups II
|03||Representations and Reducibility, Direct Sums and Tensor Products
Note: Corrected a typo in exercise H3.1(e).
|05||Permutations, Cayley's Theorem, Dihedral Group
|06||Irreps, Characters, Group Algebra
|08||Characters and the Hook Rule
|09||Lie groups and algebras, equivalence of so(3) and su(2)
|10||Matrix Identities, subalgebras, equivalence of so(3) and su(2) pt 2
|11||Lie algebras, adjoint representation, Killing form
|12||Roots and the Cartan algebra
|13||Root Systems, highest weight procedure
Note: (i) This sheet is not relevant for the admission to the exam.
(ii) Added a "positive" in H13.1(c)
Requirements for final exam
In order to be admitted to the final exam the following requirements have to be met:
- Active participation in the tutorials
- Solutions to the exercises have to be presented at least twice in the tutorials
- Approx. 50% of the credits from all exercise sheets
The module description from the syllabus is available here
Time and Place
Monday 10:15 - 12:00 & Thursday 13:15 - 14:00, Lecture Hall 1, PI
Theoretical Physics III, Basic Lectures in Mathematics
- Link to the lecture notes by Dr. Christoph Lüdeling
- H. Georgi, ``Lie Algebras In Particle Physics. From Isospin To Unified Theories''
A classic for Lie algebras. There is a new edition from 1999 which contains a nice
chapter on discrete groups as well.
- M. Hamermesh, ``Group Theory and Its Application to Physical Problems''
Another classic, in particular for finite groups and quantum mechanical applications.
- H. Weyl,``Quantum mechanics and group theory''
Weyl is one of the fathers of the use of group theory in quantum mechanics. This book is
rather old (1927), but still nicely readable.
- R. N. Cahn, ``Semisimple Lie Algebras And Their Representations''
A short treatise on Lie algebras, available online
- H. F. Jones, ``Groups, representations and physics''
A short and relatively simple book
- R. Gilmore, ``Lie Groups, Lie Algebras, and Some of Their Applications''
More mathematically oriented, contains some proofs not presented in the lecture
- W. Fulton and R Harris, ``Representation Theory: A First Course''
Relatively mathematical, but still quite accessible
- J. Fuchs and C. Schweigert, ``Symmetries, Lie Algebras And Representations:
A Graduate Course For Physicists''
Rather advanced and formal treatment, for the mathematically interested
- R. Slansky, ``Group Theory For Unified Model Building''
Invaluable because of its huge appendix of tables for Lie groups (weights,
representations, tensor products, branching rules)
- M. Nakahara, ``Geometry, topology and physics''
Covers differential geometry aspects of Lie groups. Generally recommended for every
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