Representations of Leavitt path algebras

Abstract

We study representations of a Leavitt path algebra L of a finitely separated digraph Gamma over a field. We show that the category of L-modules is equivalent to a full subcategory of quiver representations. When Gamma is a (non-separated) row-finite digraph we determine all possible finite dimensional quotients of L after giving a necessary and sufficient graph theoretic criterion for the existence of a nonzero finite dimensional quotient. This criterion is also equivalent to L having UGN (Unbounded Generating Number) as well as being algebraically amenable. We also realize the category of L-modules as a retract, hence a quotient by an explicit Serre subcategory of the category of quiver representations (that is, F Gamma-modules) via a new colimit model for M circle times(F Gamma) L. (C) 2019 Elsevier B.V. All rights reserved.