Recollements and homological dimensions

Abstract

We investigate the behavior of the homological dimensions under recollements of derived categories of algebras. In particular, we establish a series of new bounds among the selfinjective dimension or φ-dimension of the algebras linked by recollements of derived module categories.Mathematics Subject Classification (2010): 16G60; 16E35; 16G20

Recollements and tilting modules

“…Recently, gluing techniques with respect to a recollement of triangulated or abelian categories have been investigated for cotorsion pairs [6], torsion pairs [13], and so on (e.g. [16,20,21,23]). In particular, for a recollement of triangulated categories, Liu, Vitória and Yang presented explicit constructions of gluing of silting objects [12].…”