Details

Autor(en) / Beteiligte

• Karpilovsky, Gregory,

Titel

Clifford theory for group representations

Beschreibungen/Notizen

• Description based upon print version of record.
• Includes bibliography and index.
• Front Cover; Clifford Theory for Group Representations; Copyright Page; Contents; Preface; Chapter 1. Preliminaries; 1. Notation and terminology; 2. Matrix rings; 3. Artinian, noetherian and completely reducible modules; 4. The radical of modules and rings; 5. Unique decompositions; 6. Group algebras; 7. Cohomology groups; Chapter 2. Restriction to normal subgroups; 1. Induced and relatively projective modules; 2. Restriction of irreducible modules to normal subgroups; 3. Lifting idempotents; 4. Restriction of indecomposable modules to normal subgroups
• 5. Similarity with ground field extensions6. Restriction of projective covers; Chapter 3. Induction and extension from normal subgroups; 1. Group-graded algebras and crossed products; 2. Graded ideals; 3. The endomorphism ring of induced modules; 4. Inducing G-invariant modules; 5. Indecomposability of induced modules; 6. Homogeneity of induced modules; 7. Homogeneity of induced modules: an alternative approach; 8. The Loewy length of induced modules; 9. Extension from normal subgroups: basic constructions; 10. Counting nonisomorphic extensions
• 11. Projective representations and inflated modules12. Restriction and induction of absolutely irreducible modules; 13. Applications: dimensions of irreducible modules and their projective covers; 14. Extensions of modules over arbitrary fields; Bibliography; Notation; Index
• Let N be a normal subgroup of a finite group G and let F be a field. An important method for constructing irreducible FG-modules consists of the application (perhaps repeated) of three basic operations: (i) restriction to FN. (ii) extension from FN. (iii) induction from FN. This is the `Clifford Theory' developed by Clifford in 1937. In the past twenty years, the theory has enjoyed a period of vigorous development. The foundations have been strengthened and reorganized from new points of view, especially from the viewpoint of graded rings and crossed products.The purpos
• English