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It is proved in this paper that an analogous result also holds for the Lie algebra $\\BB$ related to Block type, with basis {L_{\\a,i},C|a,i\\in\\Z, i\\ge0} and relations [L_{\\a,i},L_{\\b,j}]=((i+1)\\b-(j+1)\\a)L_{\\a+\\b,i+j}+\\d_{\\a+\\b,0}\\d_{i+j,0}\\frac{\\a^3-\\a}{6}C, [C,L_{\\a,i}]=0.Namely, an irreducible quasifinite $\\BB$-module is either a highest weight module, a lowest weight module or a module of the interme"},"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":"1210.7132","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-10-26T13:08:18Z","cross_cats_sorted":[],"title_canon_sha256":"d530dc7c9cf5dae29b8cc2ab27e0c0ee9aac647140a76dd67a8d4f1ca07ff424","abstract_canon_sha256":"82b7d827dbe50eddb3336e51d6b1c1c9a99bdcbccc075a7d5c74763c827b6be6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:12.634374Z","signature_b64":"BmtqC5DDQWwMP+HDnNoWhfnQ1OVNLVdO01+2XzT1jRM7NadppskYmjP+w+8AqNo/zRgWYfSQsxolkWc5qy5QCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ecfc30659b5bf7739e57ceb9bb720b645a9ad77cc175d883770fbd77dafbea0f","last_reissued_at":"2026-05-18T03:42:12.633579Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:12.633579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Classification of quasifinite representations of a Lie algebra related to Block type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Chunguang Xia, Ying Xu, Yucai Su","submitted_at":"2012-10-26T13:08:18Z","abstract_excerpt":"A well-known theorem of Mathieu's states that a Harish-chandra module over the Virasoro algebra is either a highest weight module, a lowest weight module or a module of the intermediate series. It is proved in this paper that an analogous result also holds for the Lie algebra $\\BB$ related to Block type, with basis {L_{\\a,i},C|a,i\\in\\Z, i\\ge0} and relations [L_{\\a,i},L_{\\b,j}]=((i+1)\\b-(j+1)\\a)L_{\\a+\\b,i+j}+\\d_{\\a+\\b,0}\\d_{i+j,0}\\frac{\\a^3-\\a}{6}C, [C,L_{\\a,i}]=0.Namely, an irreducible quasifinite $\\BB$-module is either a highest weight module, a lowest weight module or a module of the interme"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7132","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1210.7132","created_at":"2026-05-18T03:42:12.633712+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.7132v1","created_at":"2026-05-18T03:42:12.633712+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.7132","created_at":"2026-05-18T03:42:12.633712+00:00"},{"alias_kind":"pith_short_12","alias_value":"5T6DAZM3LP3X","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_16","alias_value":"5T6DAZM3LP3XHHSX","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_8","alias_value":"5T6DAZM3","created_at":"2026-05-18T12:26:56.085431+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/5T6DAZM3LP3XHHSXZ243W4QLMR","json":"https://pith.science/pith/5T6DAZM3LP3XHHSXZ243W4QLMR.json","graph_json":"https://pith.science/api/pith-number/5T6DAZM3LP3XHHSXZ243W4QLMR/graph.json","events_json":"https://pith.science/api/pith-number/5T6DAZM3LP3XHHSXZ243W4QLMR/events.json","paper":"https://pith.science/paper/5T6DAZM3"},"agent_actions":{"view_html":"https://pith.science/pith/5T6DAZM3LP3XHHSXZ243W4QLMR","download_json":"https://pith.science/pith/5T6DAZM3LP3XHHSXZ243W4QLMR.json","view_paper":"https://pith.science/paper/5T6DAZM3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.7132&json=true","fetch_graph":"https://pith.science/api/pith-number/5T6DAZM3LP3XHHSXZ243W4QLMR/graph.json","fetch_events":"https://pith.science/api/pith-number/5T6DAZM3LP3XHHSXZ243W4QLMR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5T6DAZM3LP3XHHSXZ243W4QLMR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5T6DAZM3LP3XHHSXZ243W4QLMR/action/storage_attestation","attest_author":"https://pith.science/pith/5T6DAZM3LP3XHHSXZ243W4QLMR/action/author_attestation","sign_citation":"https://pith.science/pith/5T6DAZM3LP3XHHSXZ243W4QLMR/action/citation_signature","submit_replication":"https://pith.science/pith/5T6DAZM3LP3XHHSXZ243W4QLMR/action/replication_record"}},"created_at":"2026-05-18T03:42:12.633712+00:00","updated_at":"2026-05-18T03:42:12.633712+00:00"}