Gorenstein defect categories of triangular matrix algebras

We use the stable categories of some selfinjective algebras to describe the singularity categories of the cluster-tilted algebras of Dynkin type. Furthermore, in this way, we settle the problem of singularity equivalence classification of the cluster-tilted algebra of type A, D and E respectively.

The Singularity Categories of the Cluster-Tilted Algebras of Dynkin Type

Iyama constructs a class of n-complete algebras and absolute n-complete algebras by cone from finite representation type and hereditary algebras,this paper we construct a class of n-complete algebras and absolute n-complete algebras by endomorphism ring of tilting modules,so we describe n-complete algebras by other way

Iterated Tilted Algebras of Type A_n and n-complete Algebras

In this paper, we use the stable categories of some selfinjective algebras to describe the singularity categories of the cluster-tilted algebras of Dynkin type. Furthermore, in this way, we settle the problem of singularity equivalence classification of the cluster-tilted algebra of type $A$, $D$ and $E$ respectively.

The singularity categories of the Cluster-tilted algebras of Dynkin type

Let T=(RM0S) be a triangular matrix ring with R and S rings and RMS an R–S-bimodule We describe Gorenstein projective modules over T In particular, we refine a result of Enochs, Cortes-Izurdiaga,

Gorenstein projective modules and recollements over triangular matrix rings

We generalize results on existence of recollement situations of singularity categories of lower triangular Gorenstein algebras and stable monomorphism categories of Cohen–Macaulay modules.

Recollements of Singularity Categories and Monomorphism Categories

For any gentle algebra $\Lambda=KQ/\langle I\rangle$, following Kalck, we describe the quiver and the relations for its Cohen-Macaulay Auslander algebra $\mathrm{Aus}(\mathrm{Gproj}\Lambda)$ explicitly, and obtain some properties, such as $\Lambda$ is representation-finite if and only if $\mathrm{Aus}(\mathrm{Gproj}\Lambda)$ is; if $Q$ has no loop and any indecomposable $\Lambda$-module is uniquely determined by its dimension vector, then any indecomposable $\mathrm{Aus}(\mathrm{Gproj}\Lambda)$-module is uniquely determined by its dimension vector.

Cohen-Macaulay Auslander algebras of gentle algebras

For any skewed-gentle algebra, we characterize its indecomposable Gorenstein projective modules explicitly and describe its Cohen–Macaulay Auslander algebra. We prove that skewed-gentle algebras ar...

Cohen–Macaulay Auslander algebras of skewed-gentle algebras

For a gentle algebra Λ=KQ/〈I〉, we obtain an explicit description of the quiver with relations for the Cohen–Macaulay Auslander algebra Aus(GprojΛ). As a consequence, the Cohen–Macaulay Auslander al...

Ming Lu

Papers

Recollements of Singularity Categories and Monomorphism Categories

Cohen-Macaulay Auslander algebras of gentle algebras

Cohen–Macaulay Auslander algebras of skewed-gentle algebras

Cohen-macaulay auslander algebras of gentle algebras