{"paper":{"title":"A note on the isomorphism conjectures for Leavitt path algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.RA","authors_text":"R. Hazrat","submitted_at":"2012-04-16T05:39:31Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3366","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}