Finite-dimensional representations of Leavitt path algebras
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When Gamma is a row-finite digraph, we classify all finite-dimensional modules of the Leavitt path algebra L(Gamma) via an explicit Morita equivalence given by an effective combinatorial (reduction) algorithm on the digraph Gamma. The category of (unital) L(Gamma)-modules is equivalent to a full subcategory of quiver representations of Gamma. However, the category of finite-dimensional representations of L(Gamma) is tame in contrast to the finite-dimensional quiver representations of G, which are almost always wild.