# On the recursive construction of indecomposable quiver representations

@article{Weist2015OnTR, title={On the recursive construction of indecomposable quiver representations}, author={Thorsten Weist}, journal={Journal of Algebra}, year={2015}, volume={443}, pages={49-74} }

Abstract 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 an embedding of the category of representations of a new quiver into the category of representations of the original one which increases dimension vectors. Thus it can be used to construct indecomposable representations of the original quiver… Expand

#### 5 Citations

Tree normal forms for quiver representations.

- Mathematics
- 2018

We explore methods for constructing normal forms of indecomposable quiver representations. The first part of the paper develops homological tools for recursively constructing families of… Expand

Tree structures in the geometric representation theory of quivers

- Mathematics
- 2015

One of the major goals in the representation theory of quivers is the classification of isomorphism classes of representations of arbitrary quivers and the homomorphism spaces between them. Whence… Expand

Non-Schurian indecomposables via intersection theory

- Mathematics
- 2015

For an acyclic quiver with three vertices, we consider the canonical decomposition of a non-Schurian root and associate certain representations of a generalized Kronecker quiver. These… Expand

Sifat-Sifat Representasi Indekomposabel The Properties of Indecomposable Representations

- 2019

A directed graph is also called as a quiver where is a finite set of vertices, is a set of arrows, and are two maps from to . A representation of a quiver is an assignment of a vector space … Expand

Representation embeddings and the second Brauer-Thrall conjecture

- Mathematics
- 2016

We prove that over an algebraically closed field there is a representation embedding from the category of classical Kronecker-modules without the simple injective into the category of… Expand

#### References

SHOWING 1-10 OF 20 REFERENCES

Quiver representations of maximal rank type and an application to representations of a quiver with three vertices

- Mathematics
- 2008

We introduce the notion of ‘maximal rank type’ for representations of quivers, which requires certain collections of maps involved in the representation to be of maximal rank. We show that real root… Expand

General Representations of Quivers

- Mathematics
- 1992

We investigate general representations of a quiver Q. There are two main questions that we shall address. The first, which was raised by Kac, is to find the dimension vectors of the summands of a… Expand

Exceptional modules are tree modules

- Mathematics
- 1998

Abstract We consider representations of a quiver over an arbitrary field. Recall that an indecomposable representation M without self-extensions is said to be exceptional. We are going to show that… Expand

The combinatorics of quiver representations

- Mathematics
- 2006

We give a description of faces of all codimensions for the cones of weights of rings of semi-invariants of quivers. For a triple flag quiver and faces of codimension 1 this reduces to the result of… Expand

Tree modules

- Mathematics
- 2010

After stating several tools which can be used to construct indecomposable tree modules for quivers without oriented cycles, we use these methods to construct indecomposable tree modules for every… Expand

REFLECTION FUNCTORS FOR HEREDITARY ALGEBRAS

- Mathematics
- 1980

where P, Q are regular matrices of size n x n and mxm, respectively. We call the pair {n,m) the dimension type of this a + 6-tuple, and we are concerned with the determination of the dimension types… Expand

\"Uber erreichbare und baumartige unzerlegbare Darstellungen von K\"ochern

- Mathematics
- 2014

Let $A$ be a finite-dimensional algebra over an algebraically closed field. The problem of constructing indecomposable $A$-modules inductively from simple ones by means of exact sequences - called… Expand

MODULI OF REPRESENTATIONS OF FINITE DIMENSIONAL ALGEBRAS

- Mathematics
- 1994

IN this paper, we present a framework for studying moduli spaces of finite dimensional representations of an arbitrary finite dimensional algebra A over an algebraically closed field k. (The abelian… Expand

On the Canonical Decomposition of Quiver Representations

- Mathematics
- Compositio Mathematica
- 2002

Kac introduced the notion of the canonical decomposition for a dimension vector of a quiver. Here we will give an efficient algorithm to compute the canonical decomposition. Our study of the… Expand