Recollement ideals and recollements of Gorenstein defect categories

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Abstract

Let R be an Artin algebra and e ∈ R an idempotent. We study when the recollement ideal ReR induces (left) recollement of Gorenstein defect categories. As a consequence of this phenomenon, concrete triangle-equivalences between Gorenstein defect categories (resp. stable categories of Gorenstein projective modules) of R and R/ReR (resp. eRe) are obtained, and reduction conditions for Gorensteinness (resp. CM-freeness) of R and Gorenstein projective conjecture over R are provided. Finally, some applications in the context of triangular matrix algebras are given.

Keywords

recollements / recollement ideals / Gorenstein projective modules / Gorenstein defect categories / Gorenstein projective conjecture

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