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The representations of a quiver Q over a field k (the kQ-modules, where kQ is the path algebra of Q over k) have been studied for a long time, and one knows quite well the structure of the module category modkQ. It seems to be worthwhile to consider also representations of Q over arbitrary finite-dimensional k-algebras A. Here we draw the attention to the case when A=k[ϵ] is the algebra of dual numbers...
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