The 𝒰-projective resolution of simple modules over Leavitt path algebras

Abstract

Let E be a directed graph and K any field. Let LK (E) denote the Leavitt path algebra with coefficients in K. We determine the 𝒰-projective resolution of simple LK (E)-modules V[c∞] and V[p], where c∞ be a rational infinite path of E and p be an irrational infinite path of E.Let E be a directed graph and K any field. Let LK (E) denote the Leavitt path algebra with coefficients in K. We determine the 𝒰-projective resolution of simple LK (E)-modules V[c∞] and V[p], where c∞ be a rational infinite path of E and p be an irrational infinite path of E.