Group theory for Maths, Physics and Chemistry students

Group theory is an abstraction of symmetry......Page 3
Symmetry conditions......Page 4
Planar groups......Page 5
Space groups......Page 7
Formal de nition of a group......Page 10
Generation......Page 12
2.1 Cosets and Lagrange......Page 15
2.2 Quotient groups and the homomorphism theorem......Page 16
2.3.1 A Messed-Up Puzzle......Page 20
2.3.2 Permutations and their Signs......Page 22
2.3.3 No Return Possible......Page 23
2.4 Action of groups on sets......Page 26
3.1 Motivation......Page 31
space......Page 33
3.3 The Finite Subgroups of......Page 38
3.4 The Finite Subgroups of......Page 40
The notion......Page 49
Equivalence and Subrepresentations......Page 51
4.2 Decomposing Displacements......Page 56
Notes......Page 59
5.1 Characters......Page 61
5.2 Orthogonality of irreducible characters......Page 62
5.3 Character tables......Page 70
5.4 Application: symmetry of vibrations......Page 75
5.5 Notes......Page 78
6.1 Some examples of Lie groups......Page 79
6.2 Representation theory of compact Lie groups......Page 82
6.3 The irreducible representations of......Page 84
6.4 The irreducible representations of......Page 86
Bibliography......Page 91