Tilting complexes associated with a sequence of idempotents.
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 \(j\).
scientific article; zbMATH DE number 2005423