Irreducible representations of Leavitt algebras (Q2082622)

Let \(E\) be a weighted graph, \(K\) be a field, and \(L_K(E)\) be the Leavitt path algebra of \(E\) over \(K.\) The authors construct a representation graph \(F\) and a \(L_K(E)\)-module \(V_F\) associated to \(F\) and characterize representation graphs \(F\) such that \(V_F\) is simple. They show that the category of representation graphs of \(E\) is a disjoint union of subcategories each of which contains a unique universal object \(T\) such that \(V_T\) is indecomposable and a unique irreducible representation graph \(S\) such that \(V_S\) is simple. This approach generalizes Chen's construction of simple modules in the case when any edge of \(E\) has weight one and systematically produces examples of non-simple indecomposable modules.