The ubiquity of generalized cluster categories

Details The ubiquity of generalized cluster categories The ubiquity of generalized cluster categories

2009-11-25

arxiv.org/abs/0911.4819v2

Mathematics

Representation Theory

accepted for publication in Advances. Some redaction improved the paper

Scientific paper

Associated with some finite dimensional algebras of global dimension at most 2, a generalized cluster category was introduced in \cite{Ami3}, which was shown to be triangulated and 2-Calabi-Yau when it is $\Hom$-finite. By definition, the cluster categories of \cite{Bua} are a special case. In this paper we show that a large class of 2-Calabi-Yau triangulated categories, including those associated with elements in Coxeter groups from \cite{Bua2}, are triangle equivalent to generalized cluster categories. This was already shown for some special elements in \cite{Ami3}.

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