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
1 - Auslander–Reiten Theory of Finite-Dimensional Algebras
Published online by Cambridge University Press: 25 November 2023
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
Summary
We give a brief introduction to the representation theory of finite-dimensional algebras via quivers and Auslander–Reiten theory. We describe the knitting algorithm, which gives a way to compute the Auslander–Reiten quiver of many algebras of finite-representation type. We also present recent work on the description of the representation theory of gentle and skew-gentle algebras via the geometry of oriented surfaces with boundary. An application of these geometric models is given in the context of τ-tilting theory.
Keywords
- Type
- Chapter
- Information
- Modern Trends in Algebra and Representation Theory , pp. 5 - 45Publisher: Cambridge University PressPrint publication year: 2023
References
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