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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When are infinite dimensional path algebras hereditary

The title says mostly everything. Suppose we have a quiver, maybe with relations and cycles. Is it known when the path algebra modulo relations is hereditary. Especially in the case that the path ...
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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 ...
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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 ...
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Differences between quiver 1→2 and quiver 1→3←2

Could anyone tell me about the main differences between the quivers: $$ 1 \to 2 $$ and $$ 1 \to 3 \leftarrow 2 ? $$ Thanks in advance.
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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 ...