Tilting up algebras of small homological dimensions
type: Item
instance of: scholarly article
title: Tilting up algebras of small homological dimensions
zbMATH Open document ID: 1028.16006
DOI: 10.1016/S0022-4049(02)00050-6
author: Flávio U. Coelho
author: Dieter Happel
author: Luise Unger
published in: Journal of Pure and Applied Algebra
publication date: 2003-02-05T00:00:00Z
review text: For a strict shod algebra \(\Lambda\), there exists a canonical tilting module \(T\), given in terms of the Ext-projectives and Ext-injectives of the subcategories \(\mathcal R_\Lambda\) and \(\mathcal L_\Lambda\), such that \(\Gamma=\text{End}_\Lambda(T)\) has global dimension 2. Also, the authors consider two sets: \(\mathcal S\) of pairs \((\Lambda,T)\), where \(\Lambda\) is strict shod, and \(T\) is a cotilting module, satisfying certain conditions, and \(\mathcal G\) of pairs \((\Gamma,T)\), where \(\text{gldim}(\Gamma)=2\) and \(T\) is a tilting module, satisfying certain other conditions. There is a bijective correspondence between \(\mathcal S\) and \(\mathcal G\). Also, some properties of algebras in \(\mathcal G\) are discussed.
reviewed by: Gladys Chalom
Mathematics Subject Classification ID: 16G10
Mathematics Subject Classification ID: 16E10
Mathematics Subject Classification ID: 16G70
Mathematics Subject Classification ID: 16E30
zbMATH DE Number: 1864807
zbMATH Keywords: shod algebras
zbMATH Keywords: canonical tilting modules
zbMATH Keywords: special torsion pairs
zbMATH Keywords: global dimension
zbMATH Keywords: injective dimension
zbMATH Keywords: projective dimension
zbMATH Keywords: endomorphism algebras
MaRDI profile type: Publication
cites work: Torsion Theories Induced by Tilting Modules
cites work: Applications of contravariantly finite subcategories
cites work: Q4318498
cites work: Algebras with small homological dimensions
cites work: ON NON-SEMIREGULAR COMPONENTS CONTAINING PATHS FROM INJECTIVE TO PROJECTIVE MODULES
cites work: Weakly shod algebras.
cites work: Q4432954
cites work: Q4868604
cites work: Q3795770
cites work: Q3994341
cites work: A characterization of hereditary categories with tilting object
cites work: Q4206909
cites work: Q4027066
cites work: Hochschild cohomology of piecewise hereditary algebras
cites work: Hereditary abelian categories with tilting object over arbitrary base fields
cites work: Tilting in abelian categories and quasitilted algebras
cites work: Tilted Algebras
cites work: Modules of finite projective dimension and cocovers
cites work: On endomorphism algebras with small homological dimensions.
cites work: Tame algebras and integral quadratic forms
description: scientific article; zbMATH DE number 1864807