58 citations · 174 across the 20 of their papers we have counts for
12 papers · 1 filter
Total stability and Auslander-Reiten theory for Dynkin quivers
Yariana Diaz, Cody Gilbert, Ryan Kinser
This paper concerns stability functions for Dynkin quivers, in the generality introduced by Rudakov. We show that relatively few inequalities need to be satisfied for a stability f…
On algebras of finite general representation type
Ryan Kinser, Danny Lara
We introduce the notion of ``finite general representation type'' for a finite-dimensional algebra, a property related to the ``dense orbit property'' introduced by Chindris-Kinser…
Total stability functions for type quivers
Ryan Kinser
For a quiver of Dynkin type , we give a set of inequalities which are necessary and sufficient for a linear stability condition (a.k.a. central charge) $Z\c…
Tree normal forms for quiver representations
Ryan Kinser, Thorsten Weist
We explore methods for constructing normal forms of indecomposable quiver representations. The first part of the paper develops homological tools for recursively constructing famil…
Representation varieties of algebras with nodes
Ryan Kinser, András C. Lőrincz
We study the behavior of representation varieties of quivers with relations under the operation of node splitting. We show how splitting a node gives a correspondence between certa…
Moduli spaces of representations of special biserial algebras
Andrew T. Carroll, Calin Chindris, Ryan Kinser +1
We show that the irreducible components of any moduli space of semistable representations of a special biserial algebra are always isomorphic to products of projective spaces of va…
Decomposing moduli of representations of finite-dimensional algebras
Calin Chindris, Ryan Kinser
Consider a finite-dimensional algebra and any of its moduli spaces of representations. We prove a decomposition theorem which relates any irr…
Module varieties and representation type of finite-dimensional algebras
Calin Chindris, Ryan Kinser, Jerzy Weyman
In this paper we seek geometric and invariant-theoretic characterizations of (Schur-)representation finite algebras. To this end, we introduce two classes of finite-dimensional alg…
Tree modules and counting polynomials
Ryan Kinser
We give a formula for counting tree modules for the quiver S_g with g loops and one vertex in terms of tree modules on its universal cover. This formula, along with work of Hellelo…
Idempotents in representation rings of quivers
Ryan Kinser, Ralf Schiffler
For an acyclic quiver Q, we solve the Clebsch-Gordan problem for the projective representations by computing the multiplicity of a given indecomposable projective in the tensor pro…
Rank functions on rooted tree quivers
Ryan Kinser
The free abelian group R(Q) on the set of indecomposable representations of a quiver Q, over a field K, has a ring structure where the multiplication is given by the tensor product…
The rank of a quiver representation
Ryan Kinser
We define a functor which gives the "global rank of a quiver representation" and prove that it has nice properties which make it a generalization of the rank of a linear map. We de…