Related papers: Generic representations of wild quivers

The irreducible components of varieties parametrizing the finite dimensional representations of a finite dimensional algebra $\Lambda$ are explored, with regard to both their geometry and the structure of the modules they encode. Provided…

We study minimal degenerations between preprojective modules over wild quivers. Asymptotic properties of such degenerations are studied, with respect to codimension and numbers of indecomposable direct summands. We provide families of…

We apply the notion of hyperfinite families of modules to the wild path algebras of generalised Kronecker quivers $k\Theta(d)$. While the preprojective and postinjective component are hyperfinite, we show the existence of a family of…

In earlier work, the author classified rigid representations of a quiver by finitely generated free modules over a principal ideal ring. Here we extend the results to representations of a quiver by finitely generated projective modules over…

We propose a definition of expander representations of quivers, generalizing dimension (or linear algebra) expanders, as a qualitative refinement of slope stability. We prove existence of uniform expander representations for any wild quiver…

We study representation finite $K$-rational quivers over fields of characteristic $0$ and their indecomposable representations, exploiting that all Brauer obstructions for descent of representations are trivial in this case. Contrasting the…

We describe the "generic" part of the character ring of general linear groups over a finite field in terms of quiver representations.

Let $Q$ be a tame quiver of type $\widetilde{\mathbb{A}}_n$ and $\Rep(Q)$ the category of finite dimensional representations over an algebraically closed field. A representation is simply called a module. It will be shown that a regular…

A famous result by Drozd says that a finite-dimensional representation-infinite algebra is of either tame or wild representation type. But one has to make assumption on the ground field. The Gabriel-Roiter measure might be an alternative…

Any moduli space of representations of a quiver (possibly with oriented cycles) has an embedding as a dense open subvariety into a moduli space of representations of a bipartite quiver having the same type of singularities. A connected…

Let Q be a finite quiver without oriented cycles, and let k be an algebraically closed field. The main result in this paper is that there is a natural bijection between the elements in the associated Coxeter group W_Q and the cofinite…

This paper concerns preprojective representations of a finite connected valued quiver without oriented cycles. For each such representation, an explicit formula in terms of the geometry of the quiver gives a unique, up to a certain…

We show that the category of representations of the Euclidean group of orientation-preserving isometries of two-dimensional Euclidean space is equivalent to the category of representations of the preprojective algebra of infinite type A. We…

We study the essential dimension of representations of a fixed quiver with given dimension vector. We also consider the question of when the genericity property holds, i.e., when essential dimension and generic essential dimension agree. We…

It is shown that certain transformations on quiver-dimension vector pairs induce isomorphisms on the corresponding moduli spaces of quiver representations and map a stable dimension vector to a stable dimension vector. This result combined…

We give an explicit formula for wild conductor exponents of plane curves over $\mathbb{Q}_p$ in terms of standard invariants of explicit extensions of $\mathbb{Q}_p$, generalising a formula for hyperelliptic curves. To do so, we prove a…

A self-contained introduction to infinite dimensional representations over a tame hereditary algebra is provided, assuming a basic knowledge of the category of finite dimensional representations. This includes a complete description of all…

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 the finitely presented or co-presented representations, and…

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.

This paper is a survey on invariants of representations of quivers and their generalizations. We present the description of generating systems for invariants and relations between generators.