Leírás
University of Szeged, Bolyai Institute, Algebra Seminar
Abstract. Irreducible representations of both Leavitt and Cohn path algebras of an arbitrary digraph with coefficients in a commutative field introduced by Chen and Rangaswamy are constructed in several ways using both infinite paths on the right and singular vertices as well as direct limits or factors of cyclic projective ideals of the ordinary quiver algebra, respectively. A speciality of these irreducible representations becomes immediate when they are viewed as modules over the algebras generated by commuting symmetric idempotents of paths, providing a unified way to treat them. Furthermore, their defining relations are described, too, whence criteria are easily given when they are finitely presented or finite dimensional. Moreover, their endomorphism rings, annihilator primitive ideals are also computed directly.