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 LK(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 LK(E)-module S, we compute the cardinality of the set of all simple LK(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 LK(E)-modules are given. We also obtain a complete structure theorem about the Leavitt path algebra LK(E) of a finite graph E over which every simple module is finitely presented.