{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:ARDQOFLXVMJEAAPO6TGJYMDG4W","short_pith_number":"pith:ARDQOFLX","schema_version":"1.0","canonical_sha256":"0447071577ab124001eef4cc9c3066e5961747d1c8e6108c4828dc120007095f","source":{"kind":"arxiv","id":"2010.02427","version":1},"attestation_state":"computed","paper":{"title":"Urod algebras and Translation of W-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.QA"],"primary_cat":"math.RT","authors_text":"Boris Feigin, Thomas Creutzig, Tomoyuki Arakawa","submitted_at":"2020-10-06T01:43:51Z","abstract_excerpt":"In this work, we introduce Urod algebras associated to simply-laced Lie algebras as well as the concept of translation of W-algebras. Both results are achieved by showing that the quantum Hamiltonian reduction commutes with tensoring with integrable representations, that is, for $V$ and $L$ an affine vertex algebra and an integrable affine vertex algebra associated with $\\mathfrak{g}$, we have the vertex algebra isomorphism $H_{DS,f}^0(V\\otimes L)\\cong H_{DS,f}^0(V)\\otimes L$, where in the left-hand-side the Drinfeld-Sokolov reduction is taken with respect to the diagonal action of $\\widehat{\\"},"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":"2010.02427","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2020-10-06T01:43:51Z","cross_cats_sorted":["hep-th","math.QA"],"title_canon_sha256":"7de7a7073e67f1cfacaf81e953dcbe7429166d481a65d62f8fb13438da28c50d","abstract_canon_sha256":"a6283af0d9a7c1c047a119e2fae10f7d72f1a0f6262259291114954e187e4304"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:40:49.758074Z","signature_b64":"/3Pwn1jGY0UC5zJoD0hJC6If0QcddIA7gHeTmf6hFGOhdbuQV5mWMMF0p/TyNgXzeGBV3G1C75rnsjxftaC4Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0447071577ab124001eef4cc9c3066e5961747d1c8e6108c4828dc120007095f","last_reissued_at":"2026-07-05T01:40:49.757561Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:40:49.757561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Urod algebras and Translation of W-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.QA"],"primary_cat":"math.RT","authors_text":"Boris Feigin, Thomas Creutzig, Tomoyuki Arakawa","submitted_at":"2020-10-06T01:43:51Z","abstract_excerpt":"In this work, we introduce Urod algebras associated to simply-laced Lie algebras as well as the concept of translation of W-algebras. Both results are achieved by showing that the quantum Hamiltonian reduction commutes with tensoring with integrable representations, that is, for $V$ and $L$ an affine vertex algebra and an integrable affine vertex algebra associated with $\\mathfrak{g}$, we have the vertex algebra isomorphism $H_{DS,f}^0(V\\otimes L)\\cong H_{DS,f}^0(V)\\otimes L$, where in the left-hand-side the Drinfeld-Sokolov reduction is taken with respect to the diagonal action of $\\widehat{\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.02427","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2010.02427/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":"2010.02427","created_at":"2026-07-05T01:40:49.757622+00:00"},{"alias_kind":"arxiv_version","alias_value":"2010.02427v1","created_at":"2026-07-05T01:40:49.757622+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.02427","created_at":"2026-07-05T01:40:49.757622+00:00"},{"alias_kind":"pith_short_12","alias_value":"ARDQOFLXVMJE","created_at":"2026-07-05T01:40:49.757622+00:00"},{"alias_kind":"pith_short_16","alias_value":"ARDQOFLXVMJEAAPO","created_at":"2026-07-05T01:40:49.757622+00:00"},{"alias_kind":"pith_short_8","alias_value":"ARDQOFLX","created_at":"2026-07-05T01:40:49.757622+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/ARDQOFLXVMJEAAPO6TGJYMDG4W","json":"https://pith.science/pith/ARDQOFLXVMJEAAPO6TGJYMDG4W.json","graph_json":"https://pith.science/api/pith-number/ARDQOFLXVMJEAAPO6TGJYMDG4W/graph.json","events_json":"https://pith.science/api/pith-number/ARDQOFLXVMJEAAPO6TGJYMDG4W/events.json","paper":"https://pith.science/paper/ARDQOFLX"},"agent_actions":{"view_html":"https://pith.science/pith/ARDQOFLXVMJEAAPO6TGJYMDG4W","download_json":"https://pith.science/pith/ARDQOFLXVMJEAAPO6TGJYMDG4W.json","view_paper":"https://pith.science/paper/ARDQOFLX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2010.02427&json=true","fetch_graph":"https://pith.science/api/pith-number/ARDQOFLXVMJEAAPO6TGJYMDG4W/graph.json","fetch_events":"https://pith.science/api/pith-number/ARDQOFLXVMJEAAPO6TGJYMDG4W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ARDQOFLXVMJEAAPO6TGJYMDG4W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ARDQOFLXVMJEAAPO6TGJYMDG4W/action/storage_attestation","attest_author":"https://pith.science/pith/ARDQOFLXVMJEAAPO6TGJYMDG4W/action/author_attestation","sign_citation":"https://pith.science/pith/ARDQOFLXVMJEAAPO6TGJYMDG4W/action/citation_signature","submit_replication":"https://pith.science/pith/ARDQOFLXVMJEAAPO6TGJYMDG4W/action/replication_record"}},"created_at":"2026-07-05T01:40:49.757622+00:00","updated_at":"2026-07-05T01:40:49.757622+00:00"}