Tilting up algebras of small homological dimensions (Q1855449)

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.