The Integral Cluster Category
Bernhard Keller, Sarah Scherotzke

TL;DR
This paper studies integral cluster categories over principal ideal domains, revealing their favorable properties such as being describable as orbit categories, with consistent indecomposable rigid objects and transitive mutation operations.
Contribution
It demonstrates that integral cluster categories over principal ideal domains have better-behaved structural properties than previously expected.
Findings
Categories can be described as orbit categories
Indecomposable rigid objects are independent of the ground ring
Mutation operation is transitive
Abstract
Integral cluster categories of acyclic quivers have recently been used in the representation-theoretic approach to quantum cluster algebras. We show that over a principal ideal domain, such categories behave much better than one would expect: They can be described as orbit categories, their indecomposable rigid objects do not depend on the ground ring and the mutation operation is transitive.
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