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Symmetric and G-algebras: With Applications to Group Representations 1990 ed. [Hardback]

  • Formāts: Hardback, 384 pages, weight: 820 g, 384 p., 1 Hardback
  • Sērija : Mathematics and Its Applications 60
  • Izdošanas datums: 31-May-1990
  • Izdevniecība: Springer
  • ISBN-10: 0792307615
  • ISBN-13: 9780792307617
Citas grāmatas par šo tēmu:
Symmetric and G-algebras: With Applications to Group Representations 1990 ed.
  • Formāts: Hardback, 384 pages, weight: 820 g, 384 p., 1 Hardback
  • Sērija : Mathematics and Its Applications 60
  • Izdošanas datums: 31-May-1990
  • Izdevniecība: Springer
  • ISBN-10: 0792307615
  • ISBN-13: 9780792307617
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9780792307617.html
Keywords:
The theory of symmetric and G-algebras has experienced a rapid growth in the last ten to fifteen years, acquiring mathematical depth and significance and leading to new insights in group representation theory. This volume provides a systematic account of the theory together with a number of applications to modular group representation theory and block theory of group algebras. Assumes background equivalent to a standard first-year graduate algebra course. Annotation copyright Book News, Inc. Portland, Or.
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. Külshammers 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 Robinsons theorem.-
9. The Brauer morphism.-
10. Points and pointed
groups.-
11. Interior G-algebras.-
12. Bilinear forms on G-algebras.