Finite-dimensional representations of Leavitt path algebras - Özaydın, Murad; KOÇ, AYTEN (Walter De Gruyter Gmbh, Genthiner Strasse 13, D-10785 Berlin, Germany, 2018)
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.
Keywords: Leavitt path algebra; quiver representations; Morita equivalence; finite-dimensional modules; nonstable K-theory; graph monoid; dimension function; K-Theory; Graph