Journal ArticleDOI
Recollements of Singularity Categories and Monomorphism Categories
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TLDR
The authors generalize results on existence of recollement situations of singularity categories of lower triangular Gorenstein algebras and stable monomorphism categories of Cohen-Macaulay modules.Abstract:
We generalize results on existence of recollement situations of singularity categories of lower triangular Gorenstein algebras and stable monomorphism categories of Cohen–Macaulay modules.read more
Citations
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Journal ArticleDOI
Gorenstein defect categories of triangular matrix algebras
TL;DR: In this article, Chen et al. applied the technique of recollement to study the Gorenstein defect categories of triangular matrix algebras, and constructed a left recollement of the defect categories for a triangular matrix algebra under some conditions.
Journal ArticleDOI
The Singularity Categories of the Cluster-Tilted Algebras of Dynkin Type
TL;DR: In this article, the stable categories of some selfinjective algebras were used to describe the singularity categories of the cluster-tilted algebra of Dynkin type.
Posted Content
The singularity categories of the Cluster-tilted algebras of Dynkin type
TL;DR: In this paper, the stable categories of some selfinjective algebras were used to describe the singularity categories of the cluster-tilted algebra of Dynkin type.
Journal ArticleDOI
Gorenstein projective modules and recollements over triangular matrix rings
TL;DR: In this article, the authors describe Gorenstein projective modules over a triangular matrix ring with R and S rings and RMS an R-S-bimodule.
Journal ArticleDOI
Gorenstein Properties of Simple Gluing Algebras
TL;DR: For bound quiver algebras A and B, the simple gluing algebra as mentioned in this paper was proposed by identifying two vertices, and applied to cluster-tilted algebra.
References
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MonographDOI
Triangulated Categories in the Representation of Finite Dimensional Algebras
TL;DR: The use of triangulated categories in the study of representations of finite-dimensional algebras has been studied extensively in the literature as discussed by the authors, and triangulation is a useful tool in studying tilting processes.
Book
Tame Algebras and Integral Quadratic Forms
TL;DR: In this article, the construction of stable separating tubular families and tubular algebras are discussed. But they do not discuss the relation between tubular extensions and directed algesbras.
Journal ArticleDOI
Applications of contravariantly finite subcategories
Maurice Auslander,Idun Reiten +1 more