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
8 - Infinite-dimensional Lie Algebras and Their Multivariable Generalizations
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
The loop algebra, consisting of Laurent polynomials valued in a Lie algebra, admits a non-trivial central extension for each choice of invariant pairing on it. This affine Lie algebra and its cousin, the Virasoro algebra, are foundational objects in representation theory and conformal field theory. A natural question then arises: do there exist multivariable, or higher dimensional, generalizations of the affine algebra?
- Type
- Chapter
- Information
- Modern Trends in Algebra and Representation Theory , pp. 273 - 316Publisher: Cambridge University PressPrint publication year: 2023
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