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Surveys in Representation Theory of Algebras.
This volume contains selected expository lectures delivered at the annual Maurice Auslander Distinguished Lectures and International Conference over the last several years. Reflecting the diverse landscape of modern representation theory of algebras, the selected articles include: a quick introducti...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence :
American Mathematical Society,
2018.
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| Colección: | Contemporary Mathematics Ser.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Title page; Contents; Preface; On the abundance of silting modules; 1. Introduction; 2. Silting modules; 3. Cosilting modules; 4. Duality; 5. Ring epimorphisms; 6. The lattice of ring epimorphisms; Acknowledgments; References; Co-t-structures: The first decade; 0. Introduction; 1. t-structures; 2. Co-t-structures; 3. Towers which build an arbitrary object from objects of the (co- )heart; 4. Categories skewed towards t- or co-t-structures; 5. The bijections of König and Yang; 6. The silting mutation of Aihara and Iyama; Acknowledgment; References; Modules as exact functors.
- 1. Introduction2. Modules; 3. The free abelian category; 4. The context in which a module sits
- definable categories, and the functors between these; 5. When is a module over a ring?; 6. Elementary duality; 7. The bigger picture; 8. Examples; 9. Model theory and interpretations; References; A representation-theoretic approach to recollements of abelian categories; 1. Introduction; 2. Localizations, Recollements and Torsion Pairs; 3. Examples of Recollements of Abelian Categories; 4. More Examples: Recollements of Hearts; 5. Recollements of Module Categories.
- 6. Recollements of Abelian Categories and -triples7. Homological Theory of Recollements; 8. Lifting Recollements of Module Categories to the Derived Level; 9. Compatible Torsion Pairs in Recollements; 10. Recollements of Hearts and -tilt; 11. Stratifying Recollements and Hereditary Algebras; 12. Applications: Part I; 13. Applications: Part II; 14. Even More Examples: Recollements of Coherent Functors; Acknowledgments; References; Going relative with Maurice-A survey; 1. Introduction; 2. Relative homological algebra; 3. Relative homology; 4. Homologically finite subcategories.
- 5. Relative cotilting modules6. Wedderburn correspondence; 7. Dualizing direct summands of cotilting modules; 8. Applications; References; Coxeter groups and quiver representations; 1. Getting started; 2. Real and imaginary roots; 3. Reflection functors; 4. Torsion free classes and -sortable elements; References; Tree modules and limits of the approximation theory; Introduction; 1. Tree modules and their applications; 2. Tree modules and almost split sequences; Acknowledgment; References; Back Cover.