A note on singularity categories and triangular matrix algebras

Yongyun Qin

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arXiv · 2303.14091

A note on singularity categories and triangular matrix algebras

Yongyun Qin

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Abstract

Let $\Lambda = \left[\begin{array}{cc} A & 0 \\ M & B \end{array}\right] $ be an Artin algebra and $_BM_A$ a $B$-$A$-bimodule. We prove that there is a triangle equivalence $D_{sg}(\Lambda) \cong D_{sg}(A)\coprod D_{sg}(B)$ between the corresponding singularity categories if $_BM$ is semi-simple and $M_A$ is projective. As a result, we obtain a new method for describing the singularity categories of certain bounded quiver algebras.

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Yongyun Qin. 2023-03-24. A note on singularity categories and triangular matrix algebras. https://arxiv.org/abs/2303.14091

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