English

A note on the isomorphism conjectures for Leavitt path algebras

Rings and Algebras 2012-04-17 v1 K-Theory and Homology

Abstract

We relate two conjectures which have been raised for classification of Leavitt path algebras. For purely infinite simple unital Leavitt path algebras, it is conjectured that K_0 classifies them completely. For arbitrary Leavitt path algebras, it is conjectured that K^{\gr}_0 classifies them completely \cite{hazann}. We show that for two finite graphs with no sinks (which their associated Leavitt path algebras include the purely infinite simple ones) if their K^{\gr}_0-groups of their Leavitt path algebras are isomorphic then their K_0-groups are isomorphic as well.

Keywords

Cite

@article{arxiv.1204.3366,
  title  = {A note on the isomorphism conjectures for Leavitt path algebras},
  author = {R. Hazrat},
  journal= {arXiv preprint arXiv:1204.3366},
  year   = {2012}
}
R2 v1 2026-06-21T20:49:50.013Z