{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:DWS6UXDOWPQ5S4QYDHBIZPWIVP","short_pith_number":"pith:DWS6UXDO","schema_version":"1.0","canonical_sha256":"1da5ea5c6eb3e1d9721819c28cbec8abd8844f6e57f46a5b94367bc4995f483b","source":{"kind":"arxiv","id":"hep-th/0608081","version":3},"attestation_state":"computed","paper":{"title":"Deformed Kac-Moody and Virasoro Algebras","license":"","headline":"","cross_cats":["gr-qc","math-ph","math.MP","math.QA"],"primary_cat":"hep-th","authors_text":"A. M. Marques, A. P. Balachandran, A. R. Queiroz, P. Teotonio-Sobrinho","submitted_at":"2006-08-12T15:05:47Z","abstract_excerpt":"Whenever the group $\\R^n$ acts on an algebra $\\calA$, there is a method to twist $\\cal A$ to a new algebra $\\calA_\\theta$ which depends on an antisymmetric matrix $\\theta$ ($\\theta^{\\mu \\nu}=-\\theta^{\\nu \\mu}=\\mathrm{constant}$). The Groenewold-Moyal plane $\\calA_\\theta(\\R^{d+1})$ is an example of such a twisted algebra. We give a general construction to realise this twist in terms of $\\calA$ itself and certain ``charge'' operators $Q_\\mu$. For $\\calA_\\theta(\\R^{d+1})$, $Q_\\mu$ are translation generators. This construction is then applied to twist the oscillators realising the Kac-Moody (KM) a"},"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":"hep-th/0608081","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2006-08-12T15:05:47Z","cross_cats_sorted":["gr-qc","math-ph","math.MP","math.QA"],"title_canon_sha256":"17a47af6b09182d01105abe5d99d248e139d391e61a3b3c3ece84afca1c3d792","abstract_canon_sha256":"93a340c227e705d8f14a3f5761ac63914873575b9ea327647760ddbdca0b3695"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:22:42.701854Z","signature_b64":"tukr2LrzSzEEXOjkOVWs973ig85eUNYjx28Vq5e1XyqHGug50EY4jHUc0sbpVZ4SBD+BidoF0G3x7OexihU9Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1da5ea5c6eb3e1d9721819c28cbec8abd8844f6e57f46a5b94367bc4995f483b","last_reissued_at":"2026-07-04T15:22:42.701485Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:22:42.701485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Deformed Kac-Moody and Virasoro Algebras","license":"","headline":"","cross_cats":["gr-qc","math-ph","math.MP","math.QA"],"primary_cat":"hep-th","authors_text":"A. M. Marques, A. P. Balachandran, A. R. Queiroz, P. Teotonio-Sobrinho","submitted_at":"2006-08-12T15:05:47Z","abstract_excerpt":"Whenever the group $\\R^n$ acts on an algebra $\\calA$, there is a method to twist $\\cal A$ to a new algebra $\\calA_\\theta$ which depends on an antisymmetric matrix $\\theta$ ($\\theta^{\\mu \\nu}=-\\theta^{\\nu \\mu}=\\mathrm{constant}$). The Groenewold-Moyal plane $\\calA_\\theta(\\R^{d+1})$ is an example of such a twisted algebra. We give a general construction to realise this twist in terms of $\\calA$ itself and certain ``charge'' operators $Q_\\mu$. For $\\calA_\\theta(\\R^{d+1})$, $Q_\\mu$ are translation generators. This construction is then applied to twist the oscillators realising the Kac-Moody (KM) a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0608081","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/hep-th/0608081/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"hep-th/0608081","created_at":"2026-07-04T15:22:42.701549+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0608081v3","created_at":"2026-07-04T15:22:42.701549+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0608081","created_at":"2026-07-04T15:22:42.701549+00:00"},{"alias_kind":"pith_short_12","alias_value":"DWS6UXDOWPQ5","created_at":"2026-07-04T15:22:42.701549+00:00"},{"alias_kind":"pith_short_16","alias_value":"DWS6UXDOWPQ5S4QY","created_at":"2026-07-04T15:22:42.701549+00:00"},{"alias_kind":"pith_short_8","alias_value":"DWS6UXDO","created_at":"2026-07-04T15:22:42.701549+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/DWS6UXDOWPQ5S4QYDHBIZPWIVP","json":"https://pith.science/pith/DWS6UXDOWPQ5S4QYDHBIZPWIVP.json","graph_json":"https://pith.science/api/pith-number/DWS6UXDOWPQ5S4QYDHBIZPWIVP/graph.json","events_json":"https://pith.science/api/pith-number/DWS6UXDOWPQ5S4QYDHBIZPWIVP/events.json","paper":"https://pith.science/paper/DWS6UXDO"},"agent_actions":{"view_html":"https://pith.science/pith/DWS6UXDOWPQ5S4QYDHBIZPWIVP","download_json":"https://pith.science/pith/DWS6UXDOWPQ5S4QYDHBIZPWIVP.json","view_paper":"https://pith.science/paper/DWS6UXDO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-th/0608081&json=true","fetch_graph":"https://pith.science/api/pith-number/DWS6UXDOWPQ5S4QYDHBIZPWIVP/graph.json","fetch_events":"https://pith.science/api/pith-number/DWS6UXDOWPQ5S4QYDHBIZPWIVP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DWS6UXDOWPQ5S4QYDHBIZPWIVP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DWS6UXDOWPQ5S4QYDHBIZPWIVP/action/storage_attestation","attest_author":"https://pith.science/pith/DWS6UXDOWPQ5S4QYDHBIZPWIVP/action/author_attestation","sign_citation":"https://pith.science/pith/DWS6UXDOWPQ5S4QYDHBIZPWIVP/action/citation_signature","submit_replication":"https://pith.science/pith/DWS6UXDOWPQ5S4QYDHBIZPWIVP/action/replication_record"}},"created_at":"2026-07-04T15:22:42.701549+00:00","updated_at":"2026-07-04T15:22:42.701549+00:00"}