Leavitt path algebras with at most countably many irreducible representatios
Abstract
Let E be an arbitrary directed graph with no restrictions on the number of vertices and edges and let K be any field. We give necessary and sufficient conditions for the Leavitt path algebra L_K(E) to be of countable irreducible representation type, that is, we determine when L_K(E)has at most countably many distinct isomorphism classes of simple left L_K(E-modules. It is also shown that L_K(E) has dinitely many isomorphism classes of simple left modules if and only if L_K(E) is a semi-artinian von Neumann regular ring with at most finitely many ideals. Equivalent conditions on the graph E are also given. Examples are constructed showing that for each (finite or infinite) cardinal m there exists a Leavitt path algebra L having exactly m distinct isomorphism classes of simple left modules.
Keywords
Cite
@article{arxiv.1309.7917,
title = {Leavitt path algebras with at most countably many irreducible representatios},
author = {Pere Ara and Kulumani M. Rangaswamy},
journal= {arXiv preprint arXiv:1309.7917},
year = {2014}
}
Comments
This is a revised version in which we have added a new section (Section 3) where Leavitt path algebras having at most countably many isomorphism classes of simple modules are characterized