Related papers: Categorifications of Non-Integer Quivers: Type $I_…
We introduce an invariant linked to some foundational questions in geometric measure theory and provide bounds on this invariant by decomposing an arbitrary cycle into uniformly rectifiable pieces. Our invariant measures the difficulty of…
We classify flips of buildings arising from non-degenerate unitary spaces of dimension at least 4 over finite fields of odd characteristic in terms of their action on the underlying vector space. We also construct certain geometries related…
We describe presentations of braid groups of type $A$ arising from coloured quivers of mutation type $A$. We show that these can be interpreted geometrically as generalised triangulations of regular polygons.
We study finite dimensional representations of the quantum affine algebra, using geometry of quiver varieties introduced by the author. As an application, we obtain character formulas expressed in terms of intersection cohomologies of…
A quiver mutation loop is a sequence of mutations and vertex relabelings, along which a quiver transforms back to the original form. For a given mutation loop, we introduce a quantity called a partition q-series. The partition q-series are…
We determine the most general group of equivalence transformations for a family of differential equations defined by an arbitrary vector field on a manifold. We also find all invariants and differential invariants for this group up to the…
In this note, we introduce monoidal subcategories of the tensor category of finite-dimensional representations of a simply-laced quantum affine algebra, parametrized by arbitrary Dynkin quivers. For linearly oriented quivers of types A and…
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 category with E-clusters, which are a generalization of clusters.…
A systematic study of holomorphic gauge invariant operators in general $\mathcal{N}=1$ quiver gauge theories, with unitary gauge groups and bifundamental matter fields, was recently presented in [1]. For large ranks a simple counting…
The aim of this work is to offer a family of invariants that allows us to classify finite potent endomorphisms on arbitrary vector spaces, generalizing the classification of endomorphisms on finite-dimensional vector spaces. As a particular…
Let Q be a connected directed quiver with n vertices. We show that Q is representation-infinite if and only if there do exist n isomorphism classes of exceptional modules of some fixed length at least 2.
Quiver mutation plays a crucial role in the definition of cluster algebras by Fomin and Zelevinsky. It induces an equivalence relation on the set of all quivers without loops and two-cycles. A quiver is called mutation-acyclic if it is…
This paper contains some basic results on 2-groupoids, with special emphasis on computing derived mapping 2-groupoids between 2-groupoids and proving their invariance under strictification. Some of the results proven here are presumably…
For a fixed root of a quiver, it is a very hard problem to construct all or even only one indecomposable representation with this root as dimension vector. We investigate two methods which can be used for this purpose. In both cases we get…
We use recent results on matrix semi-invariants to give degree bounds on generators for the ring of semi-invariants for quivers with no oriented cycles.
We systematically determine the regular representations, quivers and representation type of all liftings of two-dimensional quantum linear spaces.
We consider $m$-cluster tilted algebras arising from quivers of Euclidean type and we give necessary and sufficient conditions for those algebras to be representation finite. For the case $\widetilde{A}$, using the geometric realization, we…
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 $A$ quiver, which generalizes the Auslander-Reiten quiver of type $A_n$ quivers. We prove that extensions,…
Functional bases of second-order differential invariants of the Euclid, Poincar\'e, Galilei, conformal, and projective algebras are constructed. The results obtained allow us to describe new classes of nonlinear many-dimensional invariant…
The notion of mixed representations of quivers can be derived from ordinary quiver representations by considering the dual action of groups on "vertex" vector spaces together with the usual action. A generating system for the algebra of…