Finite group algebras and their modules /
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| Author / Creator: | Landrock, P. (Peter) |
|---|---|
| Imprint: | Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1983. |
| Description: | x, 274 p. ; 23 cm. |
| Language: | English |
| Series: | London Mathematical Society lecture note series 84 London Mathematical Society lecture note series 84 |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/595694 |
Table of Contents:
- Preface
- Part I. The Structure of Group Algebras
- 1. Idempotents in rings. Liftings
- 2. Projective and injective modules
- 3. The radical and artinian rings
- 4. Cartan invariants and blocks
- 5. Finite dimensional algebras
- 6. Duality
- 7. Symmetry
- 8. Loewy series and socle series
- 9. The p. i. m.'s
- 10. Ext
- 11. Orders
- 12. Modular systems and blocks
- 13. Centers
- 14. R-forms and liftable modules
- 15. Decomposition numbers and Brauer characters
- 16. Basic algebras and small blocks
- 17. Pure submodules
- 18. Examples
- Part II. Indecomposable Modules and Relative Projectivity
- 1. The trace map and the Nakayama relations
- 2. Relative projectivity
- 3. Vertices and sources
- 4. Green Correspondence
- 5. Relative projective homomorphisms
- 6. Tensor products
- 7. The Green ring
- 8. Endomorphism rings
- 9. Almost split sequences
- 10. Inner products on the Green ring
- 11. Induction from normal subgroups
- 12. Permutation models
- 13. Examples
- Part III. Block Theory
- 1. Blocks, defect groups and the Brauer map
- 2. Brauer's First Main Theorem
- 3. Blocks of groups with a normal subgroup
- 4. The Extended First main Theorem
- 5. Defect groups and vertices
- 6. Generalized decomposition numbers
- 7. Subpairs
- 8. Characters in blocks
- 9. Vertices of simple modules
- 10. Defect groups
- Appendices
- References
- Index