Cargando…
Representations of algebras and related topics /
Prior to the International Congress of 1990 in Japan, a workshop on algebra was held which included some of the best known figures in this field. Many of the expository surveys given at this workshop by distinguished mathematicians are included here. Researchers into representation theory will find...
| Clasificación: | Libro Electrónico |
|---|---|
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge ; New York, NY, USA :
Cambridge University Press,
1992.
|
| Colección: | London Mathematical Society lecture note series ;
168. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Series Page; Title; Copyright; Contents; INTRODUCTION; Homologically finite subcategories; 1 Homologically finite subcategories and adjoint functors; 2 Connections with preprojective partitions; 3 Extension closed categories; 4 Contravariantly finite subcategories and tilting theory; References; Countable Generatedness Version of Rings of Pure Global Dimension Zero; INTRODUCTION; 1. PURITY AND FINITELY PRESENTED MODULES; 2. PURE-INJECTIVE MODULES AND ALGEBRAIC COMPACTNESS; 3. FINITE MATRIX SUBGROUPS AND E-PURE INJECTIVITY; 4. RINGS OF PURE GLOBAL DIMENSION ZERO; REFERENCES
- Projective Resolutions and Degree Shifting for Cohomology and Group Rings1. Introduction; 2. Homology of Koszul complexes; 3. Cohomology, varieties and complexity; 4. Tate cohomology, duality and rates of growth; 5. Marking the degree shift; 6. Variations on the theme, induction and some examples; 7. The index and quasi-regular sequences; 8. Contravariantly finite subcategories; References; MODULES OF FINITE LENGTH OVER THEIR ENDOMORPHISM RINGS; 1 THE FUNCTOR CATEGORY; 2 INJECTIVE ENVELOPES OF SIMPLE FUNCTORS; E-PURE-INJECTIVE MODULES; 4 MODULES OF FINITE ENDOLENGTH; 5 CHARACTERS; 6 DUALITY
- 7 GENERIC MODULES8 HEREDITARY ALGEBRAS; 9 LIFT CATEGORIES; REFERENCES; Pairs of semi-simple algebras (Hereditary algebras with radical-square zero); 1. A few remarks on finite dimensional associative algebras; (i) Morita equivalence; (ii) K-species and (valued) graphs; (iii) Tensor algebras; (iv) Hereditary algebras; (v) Coxeter functors, Coxeter transformations; 2. Pairs A<Band the algebra A(A, B); 3. Jones fundamental construction of a tower and its index; 4. Some examples; REFERENCES; The Module Theoretical Approach to Quasi-hereditary Algebras; 1. Definition of a quasi-hereditary algebra
- 2. Some properties of quasi-hereditary algebras3. Standardization; 4. Standard modules of small projective dimension; 5. Quasi-hereditary algebras with many projective-injective modules; 6. The preprojective algebra of type An; 7. The Auslander algebra of k[T]/(Tn); Acknowledgement; References; Matrix problems, small reduction and representations of a class of mixed Lie groups; 1 Mackey Theorem. An Example; 2 Dynkin Algebras; 3 Main Theorem. Reduction to a matrix problem; 4 Representations of bocses; 5 Small reduction; 6 Proof of the main theorem; Appendix: An example; References
- CLASSIFICATION PROBLEMS FOR MODULAR GROUP REPRESENTATIONS1. Introduction; 2. On the stable Auslander-Reiten quiver of blocks; 3. An approach to classification problems; 4. Ends of components and projective modules; 5. Tame type, results and some questions; 6. Blocks; 7. Wild type; References; Lie Algebras: Arising in Representation Theory; 1. The Comultiplication; 2. Bialgebras; 3. Hall algebras; 4. Subbialgebras; References