相关论文: Enhanced Auslander-Reiten duality and Morita theor…

Leclerc recently studied certain Frobenius categories in connection with cluster algebra structures on coordinate rings of intersections of opposite Schubert cells. We show that these categories admit a description as Gorenstein projective…

The aim of this paper is to construct singular equivalences between functor categories. As a special case, we show that there exists a singular equivalence arising from a cotilting module $T$, namely, the singularity category of $(^\perp…

We give a complete classification of differential $\mathbb{Z}$-graded homotopy categories of matrix factorizations of isolated singularities up to quasi-equivalence. This answers a question of Bernhard Keller and Evgeny Shinder. More…

We develop Tannaka duality theory for dg categories. To any dg functor from a dg category $\mathcal{A}$ to finite-dimensional complexes, we associate a dg coalgebra $C$ via a Hochschild homology construction. When the dg functor is…

We show that singular equivalences of Morita type with level between finite-dimensional Gorenstein algebras over a field preserve the (Fg) condition.

We introduce the class of dominant Auslander-Gorenstein algebras as a generalisation of higher Auslander algebras and minimal Auslander-Gorenstein algebras, and give their basic properties. We also introduce mixed (pre)cluster tilting…

We construct left and right Calabi-Yau structures on derived respectively singularity categories of symmetric orders $\Lambda$ over commutative Gorenstein rings $R$. For this, we first construct Calabi-Yau structures over $R$ by lifting…

Relative Auslander algebras were introduced and studied by Beligiannis. In this paper, we apply intermediate extension functors associated to certain recollements of functor categories to study them. In particular, we study the existence of…

We shall show that the stable categories of graded Cohen-Macaulay modules over quotient singularities have tilting objects. In particular, these categories are triangle equivalent to derived categories of finite dimensional algebras. Our…

We prove that in a 2-Calabi-Yau triangulated category, each cluster tilting subcategory is Gorenstein with all its finitely generated projectives of injective dimension at most one. We show that the stable category of its Cohen-Macaulay…

The foundations of Ringel duality for split quasi-hereditary algebras over commutative Noetherian rings are strengthened. Several descriptions and properties of the smallest resolving subcategory containing all standard modules over split…

Rings form a bicategory [Rings], with classes of bimodules as horizontal arrows, and bimodule maps as vertical arrows. The notion of Morita equivalence for rings can be translated in terms of bicategories in the following way. Two rings are…

Motivated by understanding the Brou\'e's abelian defect group conjecture from algebraic point of view, we consider the question of how to lift a stable equivalence of Morita type between arbitrary finite dimensional algebras to a derived…

This is a survey on recent developments in Cohen-Macaulay representations via tilting and cluster tilting theory. We explain triangle equivalences between the singularity categories of Gorenstein rings and the derived (or cluster)…

We contribute to the classification of finite dimensional algebras under stable equivalence of Morita type. More precisely we give a classification of the class of Erdmann's algebras of dihedral, semi-dihedral and quaternion type and obtain…

Let a finite group G act on a differential graded algebra A. This article presents necessary conditions and sufficient conditions for the skew group algebra A*G to be Calabi-Yau. In particular, when A is the Ginzburg dg algebra of a quiver…

A finite tensor category is called pointed if all its simple objects are invertible. We find necessary and sufficient conditions for two pointed semisimple categories to be dual to each other with respect to a module category. Whenever the…

Given a recollement of three proper dg algebras over a noetherian commutative ring, e.g. three algebras which are finitely generated over the base ring, which extends one step downwards, it is shown that there is a short exact sequence of…

We generalize the notions of $d$-cluster tilting pair and $d$-Auslander exact dg category to $d$-precluster tilting triple and $d$-minimal Auslander--Gorenstein exact dg category. We give a bijection between equivalence classes of…

This paper provides a systematic treatment of Gorenstein homological aspects for cleft extensions of rings. In particular, we investigate Goresnteinness, Gorenstein projective modules and singularity categories in the context of cleft…