2-recollements of singularity categories and Gorenstein defect categories over triangular matrix algebras. (Chinese. English summary) Zbl 07931749
Summary: Let \(T = \begin{pmatrix}A&M\\ 0&B\end{pmatrix}\) be a triangular matrix algebra with its corner algebras \(A\) and \(B\) Artinian and \(_AM_B\) an \(A\)-\(B\)-bimodule. The 2-recollement structures for singularity categories and Gorenstein defect categories over \(T\) are studied. Under suitable assumptions, we provide necessary and sufficient conditions for the existences of 2-recollements of singularity categories and Gorenstein defect categories over \(T\).
MSC:
| 18E30 | Derived categories, triangulated categories (MSC2010) |
| 18E35 | Localization of categories, calculus of fractions |
| 18G20 | Homological dimension (category-theoretic aspects) |
Keywords:
recollement; 2-recollement; singularity category; Gorenstein defect category; triangular matrix algebraReferences:
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