121 citations · 538 across the 72 of their papers we have counts for
14 papers · 1 filter
Artin algebras of small representation bound
Youqi Yin, Shiping Liu
This paper introduces a novel classification approach for representation-finite artin algebras in terms of the maximal length of their indecomposable modules of finite length, whic…
Auslander-Reiten theory via Nakayama duality in abelian categories
Zetao Lin, Shiping Liu
Using the Nakayama duality induced by a Nakayama functor, we provide a novel and concise account of the existence of Auslander-Reiten dualities and almost split sequences in abelia…
Representation theory of hereditary artin algebras of finite representation type
Shiping Liu, Gordana Todorov
Let be a hereditary artin algebra of finite representation type. We first determine all hammocks in the Auslander-Reiten quiver $\GaH$ of $\mmod H$, the category of finitely ge…
A Representation theoretic perspective of Koszul theory
Ales Bouhada, Min Huang, Zetao Lin +1
We discover a new connection between Koszul theory and representation theory. Let $\La$ be a quadratic algebra defined by a locally finite quiver with relations. Firstly, we give a…
Representation theory of graded algebras given by locally finite quivers
Zetao Lin, Shiping Liu
This paper aims to study graded modules over a graded algebra $\La$ given by a locally finite quiver with homogeneous relations. By constructing a graded Nakayama functor, we disco…
Almost split sequences in tri-exact categories
Shiping Liu, Hongwei Niu
We shall study the existence of almost split sequences in tri-exact categories, that is, extension-closed subcategories of triangulated categories. Our results unify and extend the…
Koszul duality for non-graded derived categories
Ales Bouhada, Min Huang, Shiping Liu
We are concerned with relating derived categories of all modules of two dual Koszul algebras defined by a locally bounded quiver. We first generalize the well known Acyclic Assembl…
Auslander-Reiten components with bounded short cycles
Shiping Liu, Jinde Xu
We study Auslander-Reiten components of an artin algebra with bounded short cycles, namely, there exists a bound for the depths of maps appearing on short cycles of non-zero non-in…
The bounded derived categories of an algebra with radical squared zero
Raymundo Bautista, Shiping Liu
Let $\La$ be an elementary locally bounded linear category over a field with radical squared zero. We shall show that the bounded derived category $D^b(\ModbLa)$ of finitely suppor…
Cluster categories of type and triangulations of the infinite strip
Shiping Liu, Charles Paquette
We first study the (canonical) orbit category of the bounded derived category of finite dimensional representations of a quiver with no infinite path, and we pay more attention on…
Another characterization of tilted algebras
Shiping Liu
We give a new characterization of tilted algebras by the existence of certain special subquivers in their Auslander-Reiten quiver. This result includes the existent characterizatio…
Standard components of a Krull-Schmidt category
Shiping Liu, Charles Paquette
We provide criteria for an Auslander-Reiten component having sections of a Krull-Schmidt category to be standard. Specializing to the category of finitely presented representations…
Representation Theory of an Infinite Quiver
Raymundo Bautista, Shiping Liu, Charles Paquette
This paper deals with the representation theory of a locally finite quiver in which the number of paths between any two given vertices is finite. We first study some properties of…
A proof of the strong no loop conjecture
Kiyoshi Igusa, Shiping Liu, Charles Paquette
The strong no loop conjecture states that a simple module of finite projective dimension over an artin algebra has no non-zero self-extension. The main result of this paper establi…