Representations and characters of groups / Gordon James and Martin Liebeck.

Format:

Book

Author/Creator:

James, G. D. (Gordon Douglas), 1945-

Contributor:

Liebeck, M. W. (Martin W.), 1954-

Edith E. Clark Endowment Fund.

Language:

English

Subjects (All):

Representations of groups.

Physical Description:

viii, 458 pages : illustrations ; 24 cm

Edition:

Second edition.

Place of Publication:

Cambridge, UK ; New York, NY : Cambridge University Press, 2001.

Summary:

This is the second edition of the popular textbook on representation theory of finite groups.

Contents:

1 Groups and homomorphisms 1

2 Vector spaces and linear transformations 14

3 Group representations 30

4 FG-modules 38

5 FG-submodules and reducibility 49

6 Group algebras 53

7 FG-homomorphisms 61

8 Maschke's Theorem 70

9 Schur's Lemma 78

10 Irreducible modules and the group algebra 89

11 More on the group algebra 95

12 Conjugacy classes 104

13 Characters 117

14 Inner products of characters 133

15 The number of irreducible characters 152

16 Character tables and orthogonality relations 159

17 Normal subgroups and lifted characters 168

18 Some elementary character tables 179

19 Tensor products 188

20 Restriction to a subgroup 210

21 Induced modules and characters 224

22 Algebraic integers 244

23 Real representations 263

24 Summary of properties of character tables 283

25 Characters of groups of order pq 288

26 Characters of some p-groups 298

27 Character table of the simple group of order 168 311

28 Character table of GL(2, q) 322

29 Permutations and characters 337

30 Applications to group theory 348

31 Burnside's Theorem 361

32 An application of representation theory to molecular vibration 367.

Notes:

Includes bibliographical references (page 454) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Edith E. Clark Endowment Fund.

ISBN:

052100392X

OCLC:

46683787

Online:

Publisher description