Symmetric and G-algebras: With Applications to Group Representations by Gregory KarpilovskySymmetric and G-algebras: With Applications to Group Representations by Gregory Karpilovsky

Symmetric and G-algebras: With Applications to Group Representations

byGregory Karpilovsky

Paperback | October 4, 2011

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Title:Symmetric and G-algebras: With Applications to Group RepresentationsFormat:PaperbackPublished:October 4, 2011Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9401067562

ISBN - 13:9789401067560

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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.