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## Representation-Infinite Quiver

Linear Algebra, Algebraic structures (Groups, Rings, Modules, etc), Galois theory, Homological Algebra
Tsakanikas Nickos
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### Representation-Infinite Quiver

Let $Q$ be a quiver. Show that if $Q$ contains a subquiver of the type $\tilde{A}_{n}$ which is not acyclic, then $Q$ is representation-infinite, i.e. there are infinitely many isomorphism classes of indecomposable representations of $Q$.