A derived equivalence between cluster equivalent algebras
Representation Theory
2011-11-21 v2
Abstract
Let be an acyclic quiver. Associated with any element of the Coxeter group of , triangulated categories were introduced in \cite{Bua2}. There are shown to be triangle equivalent to generalized cluster categories associated to algebras of global dimension in \cite{ART}. For satisfying a certain property, called co--sortable, other algebras of global dimension are constructed in \cite{AIRT} with a triangle equivalence . The main result of this paper is to prove that the algebras and are derived equivalent when is co--sortable. The proof uses the 2-APR-tilting theory introduced in \cite{IO}.
Cite
@article{arxiv.0911.5410,
title = {A derived equivalence between cluster equivalent algebras},
author = {Claire Amiot},
journal= {arXiv preprint arXiv:0911.5410},
year = {2011}
}
Comments
to appear in Journal of Algebra