A note on the isomorphism conjectures for Leavitt path algebras

JOURNAL OF ALGEBRA

卷:375

Article

Hazrat, R.

关键词: Path algebras;    Leavitt path algebras;    Strongly graded rings;   

DOI  :  10.1016/j.jalgebra.2012.11.017

来源: Elsevier

【 摘 要 】

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 (Abrams et al., 2008, 2011 [3,4]). For arbitrary unital Leavitt path algebras, it is conjectured that K-0(gr) classifies them completely (Hazrat, in press [12]). 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-0(gr)-groups of their Leavitt path algebras are isomorphic then their K-0-groups are isomorphic as well. We also provide a short proof of the fact that for a finite graph, its associated Leavitt path algebra is strongly graded if and. only if the graph has no sinks. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free