A note on singularity categories and triangular matrix algebras

2023/03/24 by Yongyun Qin, Qin, Yongyun
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2303.14091

openalex publication_date 2023/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Λ= [A · amp; 0
M · amp; B] be an Artin algebra and _BM_A a B-A-bimodule. We prove that there is a triangle equivalence D_sg(Λ) ≅ 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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