{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:3FZATJGPF46BGCAZC4KB7QFPZV","short_pith_number":"pith:3FZATJGP","schema_version":"1.0","canonical_sha256":"d97209a4cf2f3c13081917141fc0afcd7a3a82bbadea281d455f63bfaa4a5bf6","source":{"kind":"arxiv","id":"1208.3791","version":2},"attestation_state":"computed","paper":{"title":"Some weighted group algebras are operator algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Ebrahim Samei, Hun Hee Lee, Nico Spronk","submitted_at":"2012-08-18T22:42:15Z","abstract_excerpt":"Let $G$ be a finitely generated group with polynomial growth, and let $\\om$ be a weight, i.e. a sub-multiplicative function on $G$ with positive values. We study when the weighted group algebra $\\ell^1(G,\\om)$ is isomorphic to an operator algebra. We show that $\\ell^1(G,\\om)$ is isomorphic to an operator algebra if $\\om$ is a polynomial weight with large enough degree or an exponential weight of order $0<\\alpha<1$. We will demonstrate the order of growth of $G$ plays an important role in this question. Moreover, the algebraic centre of $\\ell^1(G,\\om)$ is isomorphic to a $Q$-algebra and hence s"},"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":"1208.3791","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-08-18T22:42:15Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"35ca319762d581c185d65367be434fb6d4ffd88e6c51c2cfd650c9689df79f93","abstract_canon_sha256":"f54cf28c4169280c84f0c489808fadb3073bb9207f6402ac342753a7d0d63e2b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:05.228516Z","signature_b64":"NpKIxGvB7nCvIjpzojXGaYC1xFAyxQLsOJuqiNSZ17tMgmFO0mSZ60G8n4aIGJ0aqxZ81+yoxNBBAYIqtiZCCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d97209a4cf2f3c13081917141fc0afcd7a3a82bbadea281d455f63bfaa4a5bf6","last_reissued_at":"2026-05-18T03:29:05.227862Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:05.227862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some weighted group algebras are operator algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Ebrahim Samei, Hun Hee Lee, Nico Spronk","submitted_at":"2012-08-18T22:42:15Z","abstract_excerpt":"Let $G$ be a finitely generated group with polynomial growth, and let $\\om$ be a weight, i.e. a sub-multiplicative function on $G$ with positive values. We study when the weighted group algebra $\\ell^1(G,\\om)$ is isomorphic to an operator algebra. We show that $\\ell^1(G,\\om)$ is isomorphic to an operator algebra if $\\om$ is a polynomial weight with large enough degree or an exponential weight of order $0<\\alpha<1$. We will demonstrate the order of growth of $G$ plays an important role in this question. Moreover, the algebraic centre of $\\ell^1(G,\\om)$ is isomorphic to a $Q$-algebra and hence s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3791","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1208.3791","created_at":"2026-05-18T03:29:05.227956+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.3791v2","created_at":"2026-05-18T03:29:05.227956+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3791","created_at":"2026-05-18T03:29:05.227956+00:00"},{"alias_kind":"pith_short_12","alias_value":"3FZATJGPF46B","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_16","alias_value":"3FZATJGPF46BGCAZ","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_8","alias_value":"3FZATJGP","created_at":"2026-05-18T12:26:50.516681+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3FZATJGPF46BGCAZC4KB7QFPZV","json":"https://pith.science/pith/3FZATJGPF46BGCAZC4KB7QFPZV.json","graph_json":"https://pith.science/api/pith-number/3FZATJGPF46BGCAZC4KB7QFPZV/graph.json","events_json":"https://pith.science/api/pith-number/3FZATJGPF46BGCAZC4KB7QFPZV/events.json","paper":"https://pith.science/paper/3FZATJGP"},"agent_actions":{"view_html":"https://pith.science/pith/3FZATJGPF46BGCAZC4KB7QFPZV","download_json":"https://pith.science/pith/3FZATJGPF46BGCAZC4KB7QFPZV.json","view_paper":"https://pith.science/paper/3FZATJGP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.3791&json=true","fetch_graph":"https://pith.science/api/pith-number/3FZATJGPF46BGCAZC4KB7QFPZV/graph.json","fetch_events":"https://pith.science/api/pith-number/3FZATJGPF46BGCAZC4KB7QFPZV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3FZATJGPF46BGCAZC4KB7QFPZV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3FZATJGPF46BGCAZC4KB7QFPZV/action/storage_attestation","attest_author":"https://pith.science/pith/3FZATJGPF46BGCAZC4KB7QFPZV/action/author_attestation","sign_citation":"https://pith.science/pith/3FZATJGPF46BGCAZC4KB7QFPZV/action/citation_signature","submit_replication":"https://pith.science/pith/3FZATJGPF46BGCAZC4KB7QFPZV/action/replication_record"}},"created_at":"2026-05-18T03:29:05.227956+00:00","updated_at":"2026-05-18T03:29:05.227956+00:00"}