58 citations · 174 across the 20 of their papers we have counts for
23 papers
Algebraic approaches for the decomposition of reaction networks and the determination of existence and number of steady states
Joseph M. Sauder, Bruce P. Ayati, Ryan Kinser
Chemical reaction network theory provides powerful tools for rigorously understanding chemical reactions and the dynamical systems and differential equations that represent them. A…
Actions of Hopf-Ore Extensions of Group Algebras on Path Algebras of Quivers
Elise Askelsen, Ryan Kinser
We classify the (filtered) Hopf actions of Hopf-Ore extensions of group algebras on path algebras of quivers, extending results in several other works from special cases to this ge…
Equivariant geometry of symmetric quiver orbit closures
Ryan Kinser, Martina Lanini, Jenna Rajchgot
We unify problems about the equivariant geometry of symmetric quiver representation varieties, in the finite type setting, with the corresponding problems for symmetric varieties $…
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…
Hopf actions of some quantum groups on path algebras
Ryan Kinser, Amrei Oswald
Our first collection of results parametrize (filtered) actions of a quantum Borel on the path algebra of an arbitrary (finite) quiv…
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…
Tensor algebras in finite tensor categories
Pavel Etingof, Ryan Kinser, Chelsea Walton
This paper introduces methods for classifying actions of finite-dimensional Hopf algebras on path algebras of quivers, and more generally on tensor algebras where is s…
Type D quiver representation varieties, double Grassmannians, and symmetric varieties
Ryan Kinser, Jenna Rajchgot
We unify aspects of the equivariant geometry of type quiver representation varieties, double Grassmannians, and symmetric varieties ; in particular w…
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…
Three combinatorial formulas for type A quiver polynomials and K-polynomials
Ryan Kinser, Allen Knutson, Jenna Rajchgot
We provide combinatorial formulas for the multidegree and K-polynomial of an arbitrarily oriented type A quiver locus. These formulas are generalizations of three of Knutson-Miller…
Actions of some pointed Hopf algebras on path algebras of quivers
Ryan Kinser, Chelsea Walton
We classify Hopf actions of Taft algebras T(n) on path algebras of quivers, in the setting where the quiver is loopless, finite, and Schurian. As a corollary, we see that every qui…
Type A quiver loci and Schubert varieties
Ryan Kinser, Jenna Rajchgot
We describe a closed immersion from each representation space of a type A quiver with bipartite (i.e., alternating) orientation to a certain opposite Schubert cell of a partial fla…
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 loci in representation spaces of quivers
Ryan Kinser
Rank functors on a quiver are certain additive functors from the category of representations of to the category of finite-dimensional vector spaces. Composing with the dime…
New inequalities for subspace arrangements
Ryan Kinser
For each positive integer , we give an inequality satisfied by rank functions of arrangements of subspaces. When we recover Ingleton's inequality; for higher $n…
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…