UID:
almahu_9947367826802882
Format:
1 online resource (925 p.)
ISBN:
1-282-16791-X
,
9786612167911
,
0-08-087291-3
Series Statement:
North-Holland mathematics studies ; 180
Content:
This third volume can be roughly divided into two parts. The first part is devoted to the investigation of various properties of projective characters. Special attention is drawn to spin representations and their character tables and to various correspondences for projective characters. Among other topics, projective Schur index and projective representations of abelian groups are covered. The last topic is investigated by introducing a symplectic geometry on finite abelian groups. The second part is devoted to Clifford theory for graded algebras and its application to the corresponding theo
Note:
Description based upon print version of record.
,
Front Cover; Group Representations; Copyright Page; Contents; Preface; Part I Projective Characters; Chapter 1 An Invitation to Projective Characters; 1.1. Preliminaries; 1.2. Definitions and elementary properties; 1.3. Linear independence of a-characters; 1.4. Degrees of irreducible projective characters; 1.5. Projective characters of direct products; 1.6. Class-function cocycles; 1.7. Conjugate modules and characters; 1.8. Mackey's theorems; 1.9. Induced projective characters; 1.10. Brauer's permutation lemma; 1.11. Orthogonality relations
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Chapter 2 Clifford Theory for Projective Characters2.1. Obstruction cocycles; 2.2. Restriction to normal subgroups; 2.3. Extension from normal subgroups; 2.4. Induction from normal subgroups; 2.5. Homogeneity of induced characters; 2.6. Induction over normal subgroups; Chapter 3 Correspondences for Projective Characters; 3.1. Inner products and intertwining numbers; 3.2. Induction, restriction and inner products; 3.3. Projective inductive sources; 3.4. Inductive source correspondents; 3.5. Clifford correspondents; 3.6. Restrictors and inductors; Chapter 4. Generalized Projective Characters
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4.1. Special cocycles4.2. Generalizations of Brauer's theorems; 4.3. An application; 4.4. A projective version of Artin's induction theorem; 4.5. Rational valued and real valued projective characters; Chapter 5 Projective Character Tables; 5.1. Introduction; 5.2. Conjugacy classes of Sn and An; 5.3. Conjugacy classes of double covers of Sn and An; 5.4. Spin representations and spin characters of double covers; 5.5. Spin representations and characters of double covers of Sn and An; 5.6. Spin character tables for A*n and S*n, n = 4, 5; 5.7. Dihedral groups
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5.8. Projective character tables for PSL2(q)5.9. Nonisomorphic groups with the same projective character tables; Part II Projective Representations II; Chapter 6 Splitting Fields; 6.1. Splitting fields and realizable modules; 6.2. Splitting fields for twisted group algebras; 6.3. Projective splitting fields; Chapter 7 Projective Schur Index; 7.1. General information; 7.2. Roquette's theorem; 7.3. Projective Schur index; 7.4. Schur index and projective equivalence; 7.5. A projective analogue of Roquette's theorem; Chapter 8 Projective Representations of Abelian Groups
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8.1. Symplectic abelian groups8.2. Projective representations of abelian groups; 8.3. Constructing irreducible projective representations; Part III Group-Graded Algebras; Chapter 9 Graded Modules; 9.1. Revision of basic notions; 9.2. Elementary properties of graded modules; 9.3. Graded homomorphism modules; 9.4. Graded endomorphism algebras; 9.5. Tensor products of graded modules; 9.6. Tensor products of graded algebras; 9.7. Strongly graded modules and algebras; 9.8. Invariant, conjugate and weakly invariant modules; 9.9. Miyashita's theorem; 9.10. The Jacobson radical of crossed products
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9.11. A structure theorem for strongly graded rings
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English
Additional Edition:
ISBN 0-444-87433-X
Language:
English
