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Representations and charact...

Representations and characters of groups

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

Cambridge University Press 2001

This is the second edition of the popular textbook on representation theory of finite groups. Featuring a wealth of exercises with solutions, this will be suitable for a course in representation theory. The applications of the subject will add interest for chemists and physicists as well as mathematicians

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monografia Rebiun19612091 https://catalogo.rebiun.org/rebiun/record/Rebiun19612091 m o d | cr -n--------- 010402s2001 enk ob 001 0 eng 2001028708 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 UPVA 997913408203706 UAM 991008078847904211 UPM 991005764725304212 CBUC 991001006259406712 CBUC 991010485122106709 UPCT u225033 UPCT u87815 MiAaPQ MiAaPQ MiAaPQ 512.2 512/.2 James, G. D. Gordon Douglas) 1945-) Representations and characters of groups electronic resource] Gordon James and Martin Liebeck 2nd ed Cambridge, UK New York, NY Cambridge University Press 2001 Cambridge, UK New York, NY Cambridge, UK New York, NY Cambridge University Press 1 online resource (468 p.) 1 online resource (468 p.) Text txt rdacontent computer c rdamedia online resource cr rdacarrier Cambridge mathematical textbooks Description based upon print version of record Includes bibliographical references (p. 454) and index 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 This is the second edition of the popular textbook on representation theory of finite groups. Featuring a wealth of exercises with solutions, this will be suitable for a course in representation theory. The applications of the subject will add interest for chemists and physicists as well as mathematicians Representations of groups Electronic books Liebeck, M. W. Martin W.) 1954-) 0-521-00392-X 0-521-81205-4 Cambridge mathematical textbooks

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monografia Rebiun19612091 https://catalogo.rebiun.org/rebiun/record/Rebiun19612091 m o d | cr -n--------- 010402s2001 enk ob 001 0 eng 2001028708 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 UPVA 997913408203706 UAM 991008078847904211 UPM 991005764725304212 CBUC 991001006259406712 CBUC 991010485122106709 UPCT u225033 UPCT u87815 MiAaPQ MiAaPQ MiAaPQ 512.2 512/.2 James, G. D. Gordon Douglas) 1945-) Representations and characters of groups electronic resource] Gordon James and Martin Liebeck 2nd ed Cambridge, UK New York, NY Cambridge University Press 2001 Cambridge, UK New York, NY Cambridge, UK New York, NY Cambridge University Press 1 online resource (468 p.) 1 online resource (468 p.) Text txt rdacontent computer c rdamedia online resource cr rdacarrier Cambridge mathematical textbooks Description based upon print version of record Includes bibliographical references (p. 454) and index 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 This is the second edition of the popular textbook on representation theory of finite groups. Featuring a wealth of exercises with solutions, this will be suitable for a course in representation theory. The applications of the subject will add interest for chemists and physicists as well as mathematicians Representations of groups Electronic books Liebeck, M. W. Martin W.) 1954-) 0-521-00392-X 0-521-81205-4 Cambridge mathematical textbooks