Tilting complexes associated with a sequence of idempotents.
type: Item
instance of: scholarly article
title: Tilting complexes associated with a sequence of idempotents.
zbMATH Open document ID: 1038.16006
DOI: 10.1016/S0022-4049(03)00012-4
author: Mitsuo Hoshino
author: Yoshiaki Kato
published in: Journal of Pure and Applied Algebra
publication date: 2003-11-17T00:00:00Z
review text: Okuyama proposed a very successful procedure for proving that two algebras have equivalent triangulated categories by constructing an equivalence iteratively as equivalences given by lifts of stable equivalences modifying the image of simple modules under a previously defined stable equivalence. The paper under review interprets this construction as a series of two-term tilting complexes \(T_i\) for \(i=1,\dots,n\) over rings \(B_i\) so that the endomorphism ring of \(T_i\) is \(B_{i+1}\). The complexes \(T_i\) are defined by idempotents \(e_{i+1}\) of \(e_iB_1e_i\). For the construction it is necessary to have some vanishing of \(\text{Ext}^j(A/Ae_iA,e_iA)\) for certain bounds on \(j\).
reviewed by: Alexander Zimmermann
Mathematics Subject Classification ID: 16E05
Mathematics Subject Classification ID: 18E30
Mathematics Subject Classification ID: 16D90
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 16E30
zbMATH DE Number: 2005423
zbMATH Keywords: derived equivalences
zbMATH Keywords: triangulated categories
zbMATH Keywords: stable equivalences
zbMATH Keywords: tilting complexes
zbMATH Keywords: endomorphism ring
zbMATH Keywords: idempotents
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2005423