11 citations · 28 across the 15 of their papers we have counts for
15 papers
Representations of infinite species
Raphael Bennett-Tennenhaus, Job Daisie Rock
We consider species, consisting of a possibly infinite set of rings, and bimodules between them. Simson realised the category of representations as a functor category, which we pro…
Preprojective categories of type A
Job Daisie Rock, Hugh Thomas
We introduce a continuous version of preprojective algebras of type . In particular, we are interested in the preprojective category over an open, bounded subinterval $\mathbb{I…
Categories of generalized thread quivers
Charles Paquette, Job Daisie Rock, Emine Yıldırım
We study the representation category of thread quivers and their quotients. A thread quiver is a quiver in which some arrows have been replaced by totally ordered sets. Pointwise f…
Continuous Stability Conditions of Type A and Measured Laminations of the Hyperbolic Plane
Kiyoshi Igusa, Job Daisie Rock
We introduce stability conditions (in the sense of King) for representable modules of continuous quivers of type A along with a special criteria called the four point condition. Th…
Progress on Infinite Cluster Categories Related to Triangulations of the (Punctured) Disk
Fatemeh Mohammadi, Job Daisie Rock, Francesca Zaffalon
In this mostly expository paper, we present recent progress on infinite (weak) cluster categories that are related to triangulations of the disk, with and without a puncture. First…
Admissible ideals for k-linear categories
Karin M. Jacobsen, Job D. Rock
We generalize the notion of an admissible ideal from path algebras to (small) k-linear categories that satisfy the Krull--Remak--Schmidt--Azumaya assumption. In our treatment we fi…
Continuous Nakayama Representations
Job D. Rock, Shijie Zhu
We introduce continuous analogues of Nakayama algebras. In particular, we introduce the notion of (pre-)Kupisch functions, which play a role as Kupisch series of Nakayama algebras,…
Cluster Theories and Cluster Structures of Type A
Job Daisie Rock
In the present paper we examine the relationship between several type cluster theories and structures. We define a 2D geometric model of a cluster theory, which generalizes clu…
A continuous associahedron of type A
Maitreyee C. Kulkarni, Jacob P. Matherne, Kaveh Mousavand +1
Taking a representation-theoretic viewpoint, we construct a continuous associahedron motivated by the realization of the generalized associahedron in the physical setting. We show…
Composition series of arbitrary cardinality in modular lattices and abelian categories
Eric J. Hanson, J. Daisie Rock
For a certain family of complete modular lattices, we prove a Jordan--Hölder--Scheier-like" theorem with no assumptions on cardinality or well-orderedness. This family includes bot…
Decomposition of Pointwise Finite-Dimensional S^1 Persistence Modules
Eric J. Hanson, Job D. Rock
We prove that pointwise finite-dimensional S^1 persistence modules over an arbitrary field decompose uniquely, up to isomorphism, into the direct sum of a bar code and finitely-man…
Continuous Quivers of Type A (IV) Continuous Mutation and Geometric Models of -clusters
Job Rock
This if the final paper in the seriesContinuous Quivers of Type . In this part, we generalize existing geometric models of type cluster structures to the new -clu…
Continuous Quivers of Type A (III) Embeddings of Cluster Theories
Kiyoshi Igusa, Job D. Rock, Gordana Todorov
We continue the work started in parts (I) and (II). In this part we classify which continuous type A quivers are derived equivalent and introduce the new continuous cluster categor…
Continuous Quivers of Type A (II) The Auslander-Reiten Space
Job Rock
This work is the sequel to Continuous Quivers of Type A (I). In this paper we define the Auslander-Reiten space of a continuous type quiver, which generalizes the Auslander-Rei…
Continuous quivers of type A (I) Foundations
Kiyoshi Igusa, Job D. Rock, Gordana Todorov
We generalize type quivers to continuous type quivers and prove initial results about pointwise finite-dimensional (pwf) representations. We classify the indecomosable pwf…