Surveys in representation theory of algebras : Maurice Auslander Distinguished Lectures and International Conference, April 26-May 1, 2017, April 29-May 4, 2015, April 18-23, 2013, Woods Hole Oceanographic Institute, Woods Hole, MA / Alex Martsinkovsky, Kiyoshi Igusa, Gordana Todorov, editors.

Format:

Book

Conference/Event

Contributor:

Martsinkovsky, A. (Alex), editor.

Igusa, Kiyoshi, 1949- editor.

Todorov, G. (Gordana), editor.

Conference Name:

Maurice Auslander Distinguished Lectures and International Conference.

Series:

Contemporary mathematics (American Mathematical Society). 0271-4132 716

Contemporary mathematics, 716 0271-4132

Language:

English

Subjects (All):

Representations of algebras--Congresses.

Representations of algebras.

Physical Description:

1 online resource (216 pages).

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2018]

Summary:

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 introduction to silting modules; a survey on the first decade of co-t-structures in triangulated categories; a functorial approach to the notion of module; a representation-theoretic approach to recollements in abelian categories; new examples of applications of relative homological algebra; connections between Coxeter groups and quiver representations; and recent progress on limits of approximation theory.

Contents:

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

Modules as exact functors

2. 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

A representation-theoretic approach to recollements of abelian categories

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 -triples

7. 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

Going relative with Maurice-A survey

2. Relative homological algebra

3. Relative homology

4. Homologically finite subcategories.

5. Relative cotilting modules

6. Wedderburn correspondence

7. Dualizing direct summands of cotilting modules

8. Applications

Coxeter groups and quiver representations

1. Getting started

2. Real and imaginary roots

3. Reflection functors

4. Torsion free classes and -sortable elements

Tree modules and limits of the approximation theory

Introduction

1. Tree modules and their applications

2. Tree modules and almost split sequences

Back Cover.

Notes:

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-4903-X