Book contents
- Frontmatter
- Contents
- Contributors
- Preface
- Introduction
- 1 Auslander–Reiten Theory of Finite-Dimensional Algebras
- 2 τ-tilting Theory – an Introduction
- 3 From Frieze Patterns to Cluster Categories
- 4 Infinite-dimensional Representations of Algebras
- 5 The Springer Correspondence
- 6 An Introduction to Diagrammatic Soergel Bimodules
- 7 A Companion to Quantum Groups
- 8 Infinite-dimensional Lie Algebras and Their Multivariable Generalizations
- 9 An Introduction to Crowns in Finite Groups
- 10 An Introduction to Totally Disconnected Locally Compact Groups and Their Finiteness Conditions
- 11 Locally Analytic Representations of p-adic Groups
- References
2 - τ-tilting Theory – an Introduction
Published online by Cambridge University Press: 25 November 2023
- Frontmatter
- Contents
- Contributors
- Preface
- Introduction
- 1 Auslander–Reiten Theory of Finite-Dimensional Algebras
- 2 τ-tilting Theory – an Introduction
- 3 From Frieze Patterns to Cluster Categories
- 4 Infinite-dimensional Representations of Algebras
- 5 The Springer Correspondence
- 6 An Introduction to Diagrammatic Soergel Bimodules
- 7 A Companion to Quantum Groups
- 8 Infinite-dimensional Lie Algebras and Their Multivariable Generalizations
- 9 An Introduction to Crowns in Finite Groups
- 10 An Introduction to Totally Disconnected Locally Compact Groups and Their Finiteness Conditions
- 11 Locally Analytic Representations of p-adic Groups
- References
Summary
The notion of τ-tilting theory was introduced by Adachi, Iyama and Reiten at the beginning of the last decade and quickly became one of the most active areas of research in the representation theory of finite-dimensional algebras. The aim of these notes is two-fold. On the one hand, we want to give a friendly introduction to τ-tilting theory to anyone with a small background in representation theory. On the other, we want to fill the apparent gap for a survey on the subject by collecting in one place many of the most important results in τ-tilting theory.
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- Modern Trends in Algebra and Representation Theory , pp. 46 - 108Publisher: Cambridge University PressPrint publication year: 2023