Representations and characters of groups / / Gordon James and Martin Liebeck.
This book provides a modern introduction to the representation theory of finite groups. Now in its second edition, the authors have revised the text and added much new material. The theory is developed in terms of modules, since this is appropriate for more advanced work, but considerable emphasis is placed upon constructing characters. Included here are the character tables of all groups of order less than 32, and all simple groups of order less than 1000. Applications covered include Burnside's paqb theorem, the use of character theory in studying subgroup structure and permutation groups, and how to use representation theory to investigate molecular vibration. Each chapter features a variety of exercises, with full solutions provided at the end of the book. This will be ideal as a course text in representation theory, and in view of the applications, will be of interest to chemists and physicists as well as mathematicians.
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|---|---|
| Beteiligte Person(en) | |
| Ausgabe | 2nd ed. |
| Ort, Verlag, Jahr |
Cambridge, UK ; New York, NY
: Cambridge University Press
, 2001
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| Umfang | 1 online resource (viii, 458 pages) : : digital, PDF file(s). |
| ISBN | 1-107-12542-1 1-139-63692-8 1-283-87103-3 1-139-81164-9 0-511-04524-7 0-511-81453-4 0-511-15478-X 0-511-01700-6 |
| Sprache | Englisch |
| Zusatzinfo | Title from publisher's bibliographic system (viewed on 05 Oct 2015). |
| Zusatzinfo | Cover; Half-title; Title; Copyright; Contents; Preface; 1 Groups and homomorphisms; Groups; 1.1 Examples; Subgroups; 1.2 Examples; Direct products; 1.3 Example; Functions; Homomorphisms; 1.4 Example; 1.5 Example; Cosets; 1.6 Lagrange's Theorem; Normal subgroups; 1.7 Examples; Simple groups; Kernels and images; (1.8); (1.9); 1.10 Theorem; 1.11 Example; Summary of Chapter 1; Exercises for Chapter 1; 2 Vector spaces and linear transformations; Vector spaces; (2.1); 2.2 Examples; Bases of vector spaces; 2.3 Example; (2.4); Subspaces; (2.5); 2.6 Examples; (2.7); Direct sums of subspaces 2.8 Examples(2.9); (2.10); Linear transformations; Kernels and images; (2:11); (2:12); 2.13 Examples; Invertible linear transformations; (2.14); Endomorphisms; (2.15); 2.16 Examples; Matrices; 2.17 Definition; 2.18 Examples; 2.19 Example; (2.20); (2.21); 2.22 Example; Invertible matrices; 2.23 Definition; (2.24); 2.25 Example; Eigenvalues; (2.26); 2.27 Examples; 2.28 Example; Projections; 2.29 Proposition; 2.30 Definition; 2.31 Example; 2.32 Proposition; 2.33 Example; Summary of Chapter 2; Exercises for Chapter 2; 3 Group representations; Representations; 3.1 Definition; 3.2 Examples Equivalent representations3.3 Definition; 3.4 Examples; Kernels of representations; 3.5 Definition; 3.6 Definition; 3.7 Proposition; 3.8 Examples; Summary of Chapter 3; Exercises for Chapter 3; 4 FG-modules; FG-modules; 4.1 Example; 4.2 Definition; 4.3 Definition; 4.4 Theorem; 4.5 Examples; 4.6 Proposition; (4.7); 4.8 Definitions; Permutation modules; 4.9 Example; 4.10 Definition; 4.11 Example; FG-modules and equivalent representations; 4.12 Theorem; 4.13 Example; Summary of Chapter 4; Exercises for Chapter 4; 5 FG-submodules and reducibility; FG-submodules; 5.1 Definition; 5.2 Examples Irreducible FG-modules5.3 Definition; (5.4); 5.5 Examples; Summary of Chapter 5; Exercises for Chapter 5; 6 Group algebras; The group algebra of G; 6.1 Example; 6.2 Example; 6.3 Definition; 6.4 Proposition; The regular FG-module; 6.5 Definition; 6.6 Proposition; 6.7 Example; FG acts on an FG-module; 6.8 Definition; 6.9 Examples; 6.10 Proposition; Summary of Chapter 6; Exercises for Chapter 6; 7 FG-homomorphisms; FG-homomorphisms; 7.1 Definition; 7.2 Proposition; 7.3 Examples; Isomorphic FG-modules; 7.4 Definition; 7.5 Proposition; 7.6 Theorem; (7.7); 7.8 Example; 7.9 Example; Direct sums (7.10)7.11 Proposition; 7.12 Proposition; Summary of Chapter 7; Exercises for Chapter 7; 8 Maschke's Theorem; Maschke's Theorem; 8.1 Maschke's Theorem; 8.2 Examples; (8.3); (8.4); 8.5 Example; Consequences of Maschke's Theorem; 8.6 Definition; 8.7 Theorem; 8.8 Proposition; Summary of Chapter 8; Exercises for Chapter 8; 9 Schur's Lemma; Schur's Lemma; 9.1 Schur's Lemma; 9.2 Proposition; 9.3 Corollary; 9.4 Examples; Reprensentation theory of finite abelian groups; 9.5 Proposition; 9.6 Theorem; (9.7); 9.8 Theorem; 9.9 Examples; Diagonalization; (9.10); 9.11 Proposition Some further applications of Schur's Lemma |
| Serie/Reihe | Cambridge mathematical textbooks |
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