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I was looking for a book to complement the lecture notes of the course for a more intuitive approach to the subject and full of examples (mathematical), because the handouts seem only a bunch of mathematical definitions. I've read the suggested books in the question Comprehensive book on group theory for physicists?, but that's not what I'm looking for. In fact, they either deal with a few subjects, or have too physical examples. I was looking for more geometric examples. The program of our course (the third year physics study) is this:
- Groups and axioms:
Axioms of the group. Finished and infinite group. Examples. SN groups. Continuous and discreet group.
Abelian and non-Abelian group. Unchanged subgroups and subgroups.
Isomorphism and homomorphism between groups. Simple and semi-simple groups.
- Lie groups and Lie algebra:
Lie groups and Lie algebra. Structure constant. Examples.
- Representation theory:
Representation of the group. Irreducible representations. Schur's lemma. Characters.
- Basic group / groups of homotopies:
Fundamental group and groups of general homotopies. Exact succession.
- SU Group (2), SO (3) and SU (3):
Groups and algebra of SU (2), SO (3) and SU (3). Isospin. Spin and rotations in R3. Wigner-Eckart theorem.
Tableaux of Young
- Representations of the SO group (4), of the Lorentz SO group (3.1)
and Poincaré: Group and algebra of SO (4). Vectors of Lenz and hydrogen atom. Lorentz Group.
- Roots and weights; Dynkin diagrams:
Vectors of roots and weights. Dynkin diagrams and the classification of compact groups.