A generalization of Gabriel's Galois covering functors and derived equivalences

  title={A generalization of Gabriel's Galois covering functors and derived equivalences},
  author={Hideto Asashiba},
  journal={arXiv: Representation Theory},
  • H. Asashiba
  • Published 29 July 2008
  • Mathematics
  • arXiv: Representation Theory
Covering theory, (mono)morphism categories and stable Auslander algebras
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
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
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
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.
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
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
Gluing derived equivalences together
Derived Equivalences of Actions of a Category
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.


Skew category, Galois covering and smash product of a k-category
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
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
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
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
— 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.
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