Categorification of acyclic cluster algebras: an introduction
Bernhard Keller
TL;DR
This paper introduces the foundational concepts of acyclic cluster algebras, their connection to quiver representations, and the categorification process linking cluster variables to rigid indecomposable objects.
Contribution
It provides an accessible overview of the categorification of acyclic cluster algebras and constructs the cluster category with a bijection to cluster variables.
Findings
Established the link between cluster variables and rigid indecomposable objects
Constructed the cluster category for acyclic cluster algebras
Reviewed the definition and properties of cluster algebras
Abstract
This is a concise introduction to Fomin-Zelevinsky's cluster algebras and their links with the representation theory of quivers in the acyclic case. We review the definition of cluster algebras (geometric, without coefficients), construct the cluster category and present the bijection between cluster variables and rigid indecomposable objects of the cluster category.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Algebra and Logic