On Generalized Cluster Categories
Claire Amiot (IRMA)
TL;DR
This paper surveys the development of generalized cluster categories, explaining their construction and applications in representation theory, expanding the framework of categorification of cluster algebras.
Contribution
It introduces a generalized framework for cluster categories and discusses their diverse applications in representation theory.
Findings
Generalized cluster categories extend classical cluster categories.
These categories have multiple applications in representation theory.
The survey clarifies the construction and motivation behind these generalizations.
Abstract
Cluster categories have been introduced by Buan, Marsh, Reineke, Reiten and Todorov in order to categorify Fomin-Zelevinsky cluster algebras. This survey motivates and outlines the construction of a generalization of cluster categories, and explains different applications of these new categories in representation theory.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology