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arXiv · 2008.12178

2-recollements of singualrity categories and Gorenstein defect categories over triangular matrix algebras

Huanhuan Li·Dandan Yang·Yuefei Zheng·Jiangsheng Hu
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Abstract

Let $T=(A,M,0,B)$ 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 mild assumptions, we provide necessary and sufficient conditions for the existences of 2-recollements of singularity categories and Gorenstein defect categories over $T$ relative to those of $A$ and $B$. Parts of our results strengthen and unify the corresponding work in [27,28,34].

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Huanhuan Li, Dandan Yang, Yuefei Zheng, Jiangsheng Hu. 2020-08-27. 2-recollements of singualrity categories and Gorenstein defect categories over triangular matrix algebras. https://arxiv.org/abs/2008.12178

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