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arXiv · 1012.4743

The Integral Cluster Category

Bernhard Keller·Sarah Scherotzke
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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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Bernhard Keller, Sarah Scherotzke. 2011-07-12. The Integral Cluster Category. https://doi.org/10.1093/imrn%2Frnr129

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