Symmetric and G-algebras With Applications to Group Representations
| Main Author: | |
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| Format: | eBook |
| Language: | English |
| Published: |
Dordrecht
Springer Netherlands
1990, 1990
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| Edition: | 1st ed. 1990 |
| Series: | Mathematics and Its Applications
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1. Preliminaries
- 1. Notation and terminology
- 2. Artinian, noetherian and semisimple modules
- 3. Semisimple modules
- 4. The radical and socle of modules and rings
- 5. The Krull-Schmidt theorem
- 6. Matrix rings
- 7. The Wedderburn-Artin theorem
- 8. Tensor products
- 9. Croup algebras
- 2. Frobenius and symmetric algebras
- 1. Definitions and elementary properties
- 2. Frobenius crossed products
- 3. Symmetric crossed products
- 4. Symmetric endomorphism algebras
- 5. Projective covers and injective hulls
- 6. Classical results
- 7. Frobenius uniserial algebras
- 8. Characterizations of Frobenius algebras
- 9. Characters of symmetric algebras
- 10. Applications to projective modular representations
- 11. Külshammer’s theorems
- 12. Applications
- 3. Symmetric local algebras
- 1. Symmetric local algebras A with dimFZ(A) ? 4
- 2. Some technical lemmas
- 3. Symmetric local algebras A with dimFZ(A) = 5
- 4. Applications to modular representations
- 4. G-algebras and their applications
- 1. The trace map
- 2. Permutation G-algebras
- 3. Algebras over complete noetherian local rings
- 4. Defect groups in G-algebras
- 5. Relative projective and injective modules
- 6. Vertices as defect groups
- 7. The G-algebra EndR((1H)G)
- 8. An application: The Robinson’s theorem
- 9. The Brauer morphism
- 10. Points and pointed groups
- 11. Interior G-algebras
- 12. Bilinear forms on G-algebras