Özaydın, MuradKOÇ, AYTEN2018-07-272018-07-272018-070933-77411435-5337https://doi.org/10.1515/forum-2016-0268https://hdl.handle.net/11413/2383When 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.en-USLeavitt path algebraquiver representationsMorita equivalencefinite-dimensional modulesnonstable K-theorygraph monoiddimension functionK-TheoryGraphArticle4379149000084379149000082-s2.0-850390781512-s2.0-85039078151