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We also prove that the locally finite weighted Leavitt path algebras are precisely the Noetherian ones and that $L_K(E,w)$ is locally finite iff $(E,w)$ is finite and the Gelfand-Kirillov dimension of $L_K(E,w)$ equals $0$ or $1$. Further it is shown that a locally finite weighted Leavitt path algebra is isomor"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1806.06139","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-06-15T22:00:33Z","cross_cats_sorted":[],"title_canon_sha256":"cfcd040a7e61fe06729c91ebaedee18a767bf0f59edf819c513a62d1bf409bcd","abstract_canon_sha256":"b38446961cf2559976268f2c2ec224ef2808a90527efbd0e33348850fa9bb3f4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:03.553809Z","signature_b64":"EnSIFTcuaCcVO9GpeYDZeUsjSrQudr1XYGuHHX24vXFaJD7k/Q80Qbxybq1DwYgJguaUsgMq87ollr7/gfhFDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2412ae5afc37048fd382f7b7cc636f8de0730da0add21833d3b6bc5d1b254fba","last_reissued_at":"2026-05-18T00:13:03.553057Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:03.553057Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Locally finite weighted Leavitt path algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Raimund Preusser","submitted_at":"2018-06-15T22:00:33Z","abstract_excerpt":"A group graded $K$-algebra $A=\\bigoplus\\limits_{g\\in G} A_g$ is called \"locally finite\" if $\\dim_K A_g < \\infty$ for every $g\\in G$. We characterise the weighted graphs $(E,w)$ for which the weighted Leavitt path algebra $L_K(E,w)$ is locally finite with respect to its standard grading. We also prove that the locally finite weighted Leavitt path algebras are precisely the Noetherian ones and that $L_K(E,w)$ is locally finite iff $(E,w)$ is finite and the Gelfand-Kirillov dimension of $L_K(E,w)$ equals $0$ or $1$. 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