The ubiquity of generalized cluster categories
Abstract
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}.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2009
- DOI:
- 10.48550/arXiv.0911.4819
- arXiv:
- arXiv:0911.4819
- Bibcode:
- 2009arXiv0911.4819A
- Keywords:
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- Mathematics - Representation Theory
- E-Print:
- accepted for publication in Advances. Some redaction improved the paper