Cluster-tilted algebras and their intermediate coverings
Bin Zhu
TL;DR
This paper introduces generalized cluster categories as intermediate coverings of cluster-tilted algebras, exploring their properties as Calabi-Yau triangulated categories with cluster tilting objects and analyzing their representations.
Contribution
It constructs the intermediate coverings of cluster-tilted algebras via generalized cluster categories, extending the framework of cluster theory.
Findings
Generalized cluster categories are Calabi-Yau with fractional CY-dimension.
These categories contain cluster tilting objects and subcategories.
Representation theory of these coverings is systematically studied.
Abstract
We construct the intermediate coverings of cluster-tilted algebras by defining the generalized cluster categories. These generalized cluster categories are Calabi-Yau triangulated categories with fraction CY-dimension and have also cluster tilting objects (subcategories). Furthermore we study the representations of these intermediate coverings of cluster-tilted algebras.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons