The Integral Cluster Category

Details The Integral Cluster Category The Integral Cluster Category

2010-12-21

arxiv.org/abs/1012.4743v3

International Mathematics Research Notices, July 6, 2011

Mathematics

Representation Theory

17 pages, new section added, references added

Scientific paper

10.1093/imrn/rnr129

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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