Notes on Simple Modules over Leavitt Path Algebras

Abstract

Given an arbitrary graph E and any field K, a new class of simple left modules over the Leavitt path algebra L of the graph E over K is constructed by using vertices that emit infinitely many edges. The corresponding annihilating primitive ideals are described and is used to show that these new class of simple L-modules are different from(that is non-isomorphic to) any of the previously known simple modules. 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-modules are given. We also append other information about the Leavitt path algebra L(E) of a finite graph E over which every simple left module is finitely presented.