Symmetric and G-algebras

Inhaltsverzeichnis

• 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.