Gorenstein defect categories of triangular matrix algebras

Abstract

We apply the technique of recollement to study the Gorenstein defect categories of triangular matrix algebras. First, we construct a left recollement of Gorenstein defect categories for a triangular matrix algebra under some conditions, using it, we give a categorical interpretation of the Gorenstein properties of the triangular matrix algebra obtained by X-W. Chen, B. L. Xiong and P. Zhang respectively. Second, under some additional conditions, a recollement of Gorenstein defect categories for a triangular matrix algebra is constructed. As an application, for a special kind of triangular matrix algebras, which are called simple gluing algebras, we describe their singularity categories and Gorenstein defect categories.

17 pages

References in corpus (4)

• Singularity categories of gentle algebras
• Representations of quivers over the algebra of dual numbers
• The Gorenstein defect category
• The singularity category of a quadratic monomial algebra

Cited by in corpus (1)

• Gorenstein properties of simple gluing algebras