Representation theory and beyond : Workshop and 18th International Conference on Representations of Algebras, August 8-17, 2018, Prague, Czech Republic / Jan Stovicek, Jan Trlifaj, editors.

Format:

Book

Contributor:

Stovicek, Jan, 1980- editor.

Trlifaj, Jan, editor.

Series:

Contemporary Mathematics Series

Contemporary Mathematics Series ; v.758

Language:

English

Subjects (All):

Representations of algebras--Congresses.

Representations of algebras.

Physical Description:

1 online resource (312 pages)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2020]

Language Note:

English

Summary:

This volume contains the proceedings of the Workshop and 18th International Conference on Representations of Algebras (ICRA 2018) held from August 8-17, 2018, in Prague, Czech Republic.It presents several themes of contemporary representation theory together with some new tools, such as stable \infty-categories, stable derivators, and contramodules.In the first part, expanded lecture notes of four courses delivered at the workshop are presented, covering the representation theory of finite sets with correspondences, geometric theory of quiver Grassmannians, recent applications of contramodules to tilting theory, as well as symmetries in the representation theory over an abstract stable homotopy theory.The second part consists of six more-advanced papers based on plenary talks of the conference, presenting selected topics from contemporary representation theory: recollements and purity, maximal green sequences, cohomological Hall algebras, Hochschild cohomology of associative algebras, cohomology of local selfinjective algebras, and the higher Auslander-Reiten theory studied via homotopy theory.

Contents:

Cover

Title page

Contents

Preface

Workshop Lecture Notes

Contramodules and their applications to tilting theory

Introduction

1. First lecture

2. Second lecture

3. Third lecture

References

Representations of finite sets and correspondences

1. Introduction

2. The representation theory of categories

3. Correspondences and relations

4. The algebra of permuted orders

5. The simple modules for the essential algebra

6. Correspondence functors

7. Finiteness properties

8. Stability

9. Correspondence functors and lattices

10. Fundamental functors

11. The simple correspondence functors

Three lectures on quiver Grassmannians

1. Notations

2. Quiver Grassmannians

3. Degeneration of -representations: Bongartz's theorem and applications to quiver Grassmannians

4. Examples of quiver Grassmannians

5. Quiver Grassmannians of type

6. Quiver Grassmannians of Dynkin type

7. Cell decomposition and property (S)

8. The cluster multiplication formula

9. Exercises

Acknowledgments

Higher symmetries in abstract stable homotopy theories

2. A representation-theoretic perspective on triangulated categories

3. A crash course on derivators

4. Higher symmetries

Conference Proceedings Papers

Cohomology of some local selfinjective algebras

2. The input

3. The first few syzygies of

4. A minimal projective resolution

5. The cohomology ring

6. The Hopf algebra 5 for ≥3 with ≠0

On the cohomological Hall algebra of the Kronecker quiver

1. Generalities on cohomological Hall algebras

2. The case of the Kronecker quiver

3. Proof of Theorem 1

4. Further descriptions

References.

The recollements of purity

2. Exactness conditions

3. The category of coherent functors

4. Recollements of abelian categories

5. The recollements of purity: Proof of Theorem 1

6. Equivalence of the TTF classes

Acknowledgment

Higher Auslander algebras of type and the higher Waldhausen -constructions

1. Motivation: Eilenberg-Mac Lane spaces

2. Rudiments of the theory of ∞-categories

3. The higher Waldhausen \sS-constructions

A survey on maximal green sequences

2. Mutation and green mutation

3. Applications

4. Existence and properties

5. Muller's theorem via representation theory

6. Comparing the proofs

Appendix A. Maximal chains of torsion classes, by Laurent Demonet

The Gerstenhaber bracket in Hochschild cohomology: Methods and examples

2. Computing the bracket using alternative resolutions

3. Three examples

4. Final remarks

Back Cover.

Notes:

Includes bibliographical references.

Description based on print version record.

Description based on publisher supplied metadata and other sources.

OCLC:

1235598724