A quiver is an oriented graph which might contain multiple edges and loops. The terminology is used in representation-theory of finite dimensional algebras, where one considers functors from this graph, viewed as a category, to the category of vector spaces.

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Is there a name for this acyclic quiver?

Sorry for the trivial question, but I don't know much about the subject and don't seem to be able to come up with much by Googling. Is there an established name for quivers of the form $$\require{...
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Quiver algebra as a wreath product?

I'm having trouble understanding a definition of a quiver Hecke algebra. Suppose $k$ is a commutative ring, and $\Omega$ a finite set. We build a quiver $Q_{\Omega,n}$ with vertex set $\Omega^n$. ...
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What can we do about the indecomposable representations of wild quivers and wild algebras?

I know that using finite number of parameters we can not describe indecomposable modules of wild quivers, but is it possible for us to describe them using infinitely many parameters for at least some ...
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Multidegree semi-invariants for quiver representations

Given a quiver Q=($Q_0,Q_1$) ($Q_0$ is the set of vertices and $Q_1$ is the set of arrows) and a dimension vector $\alpha$, the coordinate ring may be written as $\bigotimes_{a \in Q_1}k[Hom(k^{\alpha(...
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Auslander-Reiten theory: exercise $23.b$ of 'Elements of the Representation Theory of Associative Algebras'

I am solving exercise $23.b$ of chapter IV of 'Elements of the representation theory of associative algebras' by Assem, Simson and Skowronski. The question is the following: Consider the following ...
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Proposition 2.3 of Quiver Representations by Ralf Schiffler

I'm trying to prove proposition 2.3 of Quiver Representations by Ralf Schiffler. To any vertex $i$ finite acyclic quiver $Q$ we can associate the indecomposable projective $P(i)$, this proposition ...
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How to recognize a monomial quiver algebra

Given a basic split finite dimensional algebra $A$ over a field K, A is isomorphic to $KQ/I_1$, for some quiver Q and a minimal(meaning it is generated by relations $x_i$, such that no relation is ...
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Why Jacobson, but not the left (right) maximals individually?

When we are working with Path Algebras, it does not need very sophisticated tools to prove that for a finite, connected, acyclic quiver $Q$, the Jacobson Radical of $KQ$ is nothing but the arrow ideal....
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Theorem $2.15$ of Quiver Representations by Ralf Schiffler.

I'm reading the proof of theorem $2.15$ of Quiver Representations by Karl Schiffler. The author states the following: Let $Q$ be a finite acyclic quiver, $M=(\left\{M_i\right\}_{i\in Q_0}, \left\{\...
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Finding all admissible Ideals of a given quiver with gap/qpa.

Let Q be a given finite quiver (with 1 point to make things easier for a start if necessary, for definitions see https://en.wikipedia.org/wiki/Quiver_%28mathematics%29 ) and fix a finite field K. Let ...
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Reference request: bounded derived categories and their Auslander-Reiten quivers

I have some knowledge of Auslander-Reiten theory, tilting theory, derived categories and triangulated categories though I still find most proofs using derived categories in "Tilting Theory and Cluster ...
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Mutations of an $A_n$ quiver to reach $A_n$ straight orientation

(1)For a quiver $A_n$ of arbitrary orientation does there exist a finite sequence of quiver mutations that can mutate it to $A_n$ straight orientation $1\rightarrow 2\rightarrow\cdots\rightarrow n$ or ...
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Characters of Linear Algebraic Groups

Reading about the semi-invariants of quivers, I see a fact which is frequently referred to in the literature, and is assumed to be trivial. However, I don't see that very easily. So, I was wondering ...