Symmetric and G-algebras [electronic resource] : With Applications to Group Representations /

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.

Bibliographic Details

Main Authors:	Karpilovsky, Gregory. author., SpringerLink (Online service)
Format:	Texto biblioteca
Language:	eng
Published:	Dordrecht : Springer Netherlands, 1990
Subjects:	Mathematics., Algebra., Associative rings., Rings (Algebra)., Group theory., Associative Rings and Algebras., Group Theory and Generalizations.,
Online Access:	http://dx.doi.org/10.1007/978-94-009-0597-9
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