On simple modules over Leavitt path algebras

Given an arbitrary graph E and any field K, a new class of simple modules over the Leavitt path algebra L-K(E) is constructed by using vertices that emit infinitely many edges in E. The corresponding annihilating primitive ideals are also described. Given a fixed simple L-K(E)-module S, we compute the cardinality of the set of all simple L-K(E)-modules isomorphic to S. Using a Boolean subring of idempotents induced by paths in E, bounds for the cardinality of the set of distinct isomorphism classes of simple L-K(E)-modules are given. We also obtain a complete structure theorem about the Leavitt path algebra L-K(E) of a finite graph E over which every simple module is finitely presented. (C) 2014 Elsevier Inc. All rights reserved.