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

2020/08/27 by Huanhuan Li, Dandan Yang, Li, Huanhuan +5
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #K-Theory and Homology (math.KT) #Nonlinear Waves and Solitons #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2008.12178

openalex publication_date 2020/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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].

Citations

• Stable module theory

Related

• Gorenstein defect categories of triangular matrix algebras
• Gorenstein projective modules and recollements over triangular matrix rings
• Symmetric recollements induced by bimodule extensions
• Lifting of recollements and Gorenstein projective modules
• Functor categories, Recollements, Triangular Matrix category