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Representation-Infinite Quiver

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

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Post by Tsakanikas Nickos » Wed Jan 27, 2016 9:10 pm

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 \( Q \).
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