Moduli of representations of Leavitt path algebras

We transpose Jones' technology and the authors' C*-algebraic techniques to study representations of the Leavitt path algebra L (over an arbitrary row-finite graph) by using its quiver algebra A. We establish an equivalence of categories between certain full subcategories of Rep(A) and Rep(L) that preserves irreducibility and indecomposability. We define a dimension function on Rep(L), and for each finite dimension we provide a moduli space for the irreducible classes by transporting structures of King and Nakajima on quiver representations. Our techniques are both explicit and functorial.