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.
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}
}