49 Citations
Covering theory, (mono)morphism categories and stable Auslander algebras
- Mathematics
- 2020
Let $\mathcal{A}$ be a locally bounded $k$-category and $G$ a torsion-free group of $k$-linear automorphisms of $\mathcal{A}$ acting freely on the objects of $\mathcal{A},$ and…
On Frobenius (completed) orbit categories
- Mathematics
- 2015
Let ${\mathcal E}$ be a Frobenius category, ${\mathcal P}$ its subcategory of projective objects and $F:{\mathcal E} \to {\mathcal E}$ an exact automorphism. We prove that there is a fully faithful…
On Standard Derived Equivalences of Orbit Categories
- Mathematics
- 2015
Let k be a commutative ring, A$\mathcal {A}$ and ℬ$\mathcal {B}$ – two k-linear categories with an action of a group G. We introduce the notion of a standard G-equivalence from Kpbℬ$\mathcal…
Singularity categories of locally bounded categories with radical square zero
- Mathematics
- 2019
This paper studies several singularity categories of a locally bounded $k-$linear category $\mathscr{C}$ with radical square zero. Following the work of Bautista and Liu [6], we give a complete…
Singularity categories of representations of quivers over local rings.
- Mathematics
- 2017
Let $\Lambda$ be a finite-dimensional algebra with finite global dimension, $R_k=K[X]/(X^k)$ be the $\mathbb{Z}$-graded local ring with $k\geq1$, and $\Lambda_k=\Lambda\otimes_K R_k$. We consider the…
Gorenstein modifications and \mathds{𝑄}-Gorenstein rings
- Mathematics
- 2016
Let $R$ be a Cohen--Macaulay normal domain with a canonical module $\omega_R$. It is proved that if $R$ admits a noncommutative crepant resolution (NCCR), then necessarily it is…
Derived Equivalences of Actions of a Category
- MathematicsAppl. Categorical Struct.
- 2013
This work investigates derived equivalences of those oplax functors, and establishes a Morita type theorem for them, which gives a base of investigations of derived equivalence of Grothendieck constructions of those Oplaxfunctors.
On a family of Caldero–Chapoton algebras that have the Laurent phenomenon
- MathematicsJournal of Algebra
- 2019
References
SHOWING 1-10 OF 28 REFERENCES
Skew category, Galois covering and smash product of a k-category
- Mathematics
- 2003
In this paper we consider categories over a commutative ring provided either with a free action or with a grading of a not necessarily finite group. We define the smash product category and the skew…
Graphs with relations, coverings and group-graded algebras
- Mathematics
- 1983
The paper studies the interrelationship between coverings of finite directed graphs and gradings of the path algebras associated to the directed graphs. To include gradings of all basic…
Group-graded rings and duality
- Mathematics
- 1985
We give an alternative construction of the duality between finite group actions and group gradings on rings which was shown by Cohen and Montgomery in [1]. This duality is then used to extend known…
On triangulated orbit categories
- Mathematics
- 2005
We show that the category of orbits of the bounded derived category of a hereditary category under a well-behaved autoequivalence is canonically triangulated. This answers a question by A. Buan, R.…
Deriving DG categories
- Mathematics
- 1994
— We investigate the (unbounded) derived category of a differential Z-graded category (=DG category). As a first application, we deduce a "triangulated analogue" (4.3) of a theorem of Freyd's [5],…
Galois coverings, Morita equivalence and smash extensions of categories over a field.
- Mathematics
- 2005
Algebras over a field k generalize to categories over k in order to considers Galois coverings. Two theories presenting analogies, namely smash extensions and Galois coverings with respect to a…