A note on the regular ideals of Leavitt path algebras
Rings and Algebras
2021-07-22 v3
Abstract
We show that, for an arbitrary graph, a regular ideal of the associated Leavitt path algebra is also graded. As a consequence, for a row-finite graph, we obtain that the quotient of the associated Leavitt path by a regular ideal is again a Leavitt path algebra and that Condition~(L) is preserved by quotients by regular ideals. Furthermore, we describe the vertex set of a regular ideal and make a comparison between the theory of regular ideals in Leavitt path algebras and in graph C*-algebras.
Keywords
Cite
@article{arxiv.2006.03634,
title = {A note on the regular ideals of Leavitt path algebras},
author = {Daniel Gonçalves and Danilo Royer},
journal= {arXiv preprint arXiv:2006.03634},
year = {2021}
}
Comments
First version has been significantly improved. We thank the journal referee and Dr. Pere Ara for their insightfull suggestions