5 citations · 17 across the 14 of their papers we have counts for
22 papers
Semi-Invariant Rings: UFD and Codimension One Orbits
Charles Paquette, Deepanshu Prasad, David Wehlau
Let be a finite dimensional associative -algebra over an algebraically closed field of characteristic zero. To , we can associate its basic form tha…
Biserial algebras and generic bricks
Kaveh Mousavand, Charles Paquette
We consider generic bricks and use them in the study of arbitrary biserial algebras over algebraically closed fields. For a biserial algebra , we show that is brick-infinite…
Representations of free products of semisimple algebras via quivers
Andrew Buchanan, Ivan Dimitrov, Olivia Grace +3
Let denote an algebraically closed field and a free product of finitely many semisimple associative -algebras. We associate to a finite acyclic qui…
Minimal (-)tilting infinite algebras
Kaveh Mousavand, Charles Paquette
Motivated by a new conjecture on the behavior of bricks, we start a systematic study of minimal -tilting infinite algebras. In particular, we treat minimal -tilting infinite…
Subregular -rings of Coxeter systems via quiver path algebras
Ivan Dimitrov, Charles Paquette, David Wehlau +1
We study the subregular -ring of a Coxeter system , a subring of Lusztig's -ring. We prove that is isomorphic to a quotient of the path algebra of the doub…
Completions of discrete cluster categories of type
Charles Paquette, Emine Yildirim
We complete the discrete cluster categories of type as defined by Igusa and Todorov, by embedding such a discrete cluster category inside a larger one, and then taking…
Idempotent reduction for the finitistic dimension conjecture
Diego Bravo, Charles Paquette
In this note, we prove that if is an Artin algebra with a simple module of finite projective dimension, then the finiteness of the finitistic dimension of implies that…
Generators versus projective generators in abelian categories
Charles Paquette
Let be an essentially small abelian category. We prove that if admits a generator with right artinian, then $\mathcal{A…
Homological behavior of idempotent subalgebras and Ext algebras
Colin Ingalls, Charles Paquette
Let be a (left and right) Noetherian ring that is semiperfect. Let be an idempotent of and consider the ring and the semi-simple right -module $S_e…
Group actions on cluster algebras and cluster categories
Charles Paquette, Ralf Schiffler
We introduce admissible group actions on cluster algebras, cluster categories and quivers with potential and study the resulting orbit spaces. The orbit space of the cluster algebr…
Isotropic Schur roots
Charles Paquette, Jerzy Weyman
In this paper, we study the isotropic Schur roots of an acyclic quiver with vertices. We study the perpendicular category of a dimension vector and giv…
Irreducible morphisms and locally finite dimensional representations
Charles Paquette
Let be a Hom-finite additive Krull-Schmidt -category where is an algebraically closed field. Let denote the category of locally finite…
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…
Accumulation points of real Schur roots
Charles Paquette
Let be an algebraically closed field and be an acyclic quiver with vertices. Consider the category of finite dimensional representations of over .…
Homological dimensions for co-rank one idempotent subalgebras
Colin Ingalls, Charles Paquette
Let be an algebraically closed field and be a (left and right) Noetherian associative -algebra. Assume further that is either positively graded or semiperfect (this…
Semi-stable subcategories for Euclidean quivers
Colin Ingalls, Charles Paquette, Hugh Thomas
In this paper, we study the semi-stable subcategories of the category of representations of a Euclidean quiver, and the possible intersections of these subcategories. Contrary to t…
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…
Almost split sequences and approximations
Shiping Liu, Puiman Ng, Charles Paquette
Let A be an exact category, that is, an extension-closed full subcategory of an abelian category. Firstly, we give some necessary and sufficient conditions for A to have almost spl…
On the Auslander-Reiten quiver of the representations of an infinite quiver
Charles Paquette
Let Q be a strongly locally finite quiver and denote by rep(Q) the category of locally finite dimensional representations of Q over some fixed field k. The main purpose of this pap…
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 non-existence theorem for almost split sequences
Charles Paquette
Let k be a field, Q a quiver with countably many vertices and I an ideal of kQ such that kQ/I has finite dimensional Hom-spaces. In this note, we prove that there is no almost spli…
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…