Leavitt path algebras with at most countably many irreducible representations

Pere Ara, Kulumani M. Rangaswamy

Research output: Contribution to journalArticleResearchpeer-review

4 Citations (Scopus)

Abstract

© 2015 European Mathematical Society. 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 LK(E) to be of countable irreducible representation type, that is, we determine when LK(E) has at most countably many distinct isomorphism classes of simple left LK(E)-modules. It is also shown that LK(E) has finitely many isomorphism classes of simple left modules if and only if LK (E) is a semi-artinian von Neumann regular ring with finitely many ideals. Equivalent conditions on the graph E are also given. Examples are constructed showing that for each (finite or infinite) cardinal κ there exists a Leavitt path algebra LK(E) having exactly κ distinct isomorphism classes of simple right modules.
Original languageEnglish
Pages (from-to)1263-1276
JournalRevista Matematica Iberoamericana
Volume31
Issue number4
DOIs
Publication statusPublished - 1 Jan 2015

Keywords

  • Irreducible representation
  • Leavitt path algebra
  • Socle
  • Von Neumann regular

Fingerprint Dive into the research topics of 'Leavitt path algebras with at most countably many irreducible representations'. Together they form a unique fingerprint.

Cite this