English

A derived equivalence between cluster equivalent algebras

Representation Theory 2011-11-21 v2

Abstract

Let QQ be an acyclic quiver. Associated with any element ww of the Coxeter group of QQ, triangulated categories \SubΛw\underline{\Sub}\Lambda_w were introduced in \cite{Bua2}. There are shown to be triangle equivalent to generalized cluster categories \CcΓw\Cc_{\Gamma_w} associated to algebras Γw\Gamma_w of global dimension 2\leq 2 in \cite{ART}. For ww satisfying a certain property, called co-cc-sortable, other algebras AwA_w of global dimension 2\leq 2 are constructed in \cite{AIRT} with a triangle equivalence \CcAw\SubΛw\Cc_{A_w}\simeq \underline{\Sub}\Lambda_w. The main result of this paper is to prove that the algebras Γw\Gamma_w and AwA_w are derived equivalent when ww is co-cc-sortable. The proof uses the 2-APR-tilting theory introduced in \cite{IO}.

Keywords

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

R2 v1 2026-06-21T14:17:14.610Z