Book contents
- Frontmatter
- Contents
- Preface
- 1 Groups and homorphisms
- 2 Vector spaces and linear transformations
- 3 Group representations
- 4 FG-modules
- 5 FG-submodules and reducibility
- 6 Group algebras
- 7 FG-homomorphisms
- 8 Maschke's Theorem
- 9 Schur's Lemma
- 10 Irreducible modules and the group algebra
- 11 More on the group algebra
- 12 Conjugacy classes
- 13 Characters
- 14 Inner products of characters
- 15 The number of irreducible characters
- 16 Character tables and orthogonality relations
- 17 Normal subgroups and lifted characters
- 18 Some elementary character tables
- 19 Tensor products
- 20 Restriction to a subgroup
- 21 Induced modules and characters
- 22 Algebraic integers
- 23 Real representations
- 24 Summary of properties of character tables
- 25 Characters of groups of order pq
- 26 Characters of some p-groups
- 27 Character table of the simple group of order 168
- 28 Character table of GL(2, q)
- 29 Permutations and characters
- 30 Applications to group theory
- 31 Burnside's Theorem
- 32 An application of representation theory to molecular vibration
- Solutions to exercises
- Bibligraphy
- Index
11 - More on the group algebra
Published online by Cambridge University Press: 05 June 2012
Book contents
- Frontmatter
- Contents
- Preface
- 1 Groups and homorphisms
- 2 Vector spaces and linear transformations
- 3 Group representations
- 4 FG-modules
- 5 FG-submodules and reducibility
- 6 Group algebras
- 7 FG-homomorphisms
- 8 Maschke's Theorem
- 9 Schur's Lemma
- 10 Irreducible modules and the group algebra
- 11 More on the group algebra
- 12 Conjugacy classes
- 13 Characters
- 14 Inner products of characters
- 15 The number of irreducible characters
- 16 Character tables and orthogonality relations
- 17 Normal subgroups and lifted characters
- 18 Some elementary character tables
- 19 Tensor products
- 20 Restriction to a subgroup
- 21 Induced modules and characters
- 22 Algebraic integers
- 23 Real representations
- 24 Summary of properties of character tables
- 25 Characters of groups of order pq
- 26 Characters of some p-groups
- 27 Character table of the simple group of order 168
- 28 Character table of GL(2, q)
- 29 Permutations and characters
- 30 Applications to group theory
- 31 Burnside's Theorem
- 32 An application of representation theory to molecular vibration
- Solutions to exercises
- Bibligraphy
- Index
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- Representations and Characters of Groups , pp. 95 - 103Publisher: Cambridge University PressPrint publication year: 2001