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Let $\\mathcal{L}_{\\mathfrak{q}}$ be the Lusztig algebra associated to $\\mathcal{B}_{\\mathfrak{q}}$, see http://arxiv.org/abs/1501.04518. We present $\\mathcal{L}_{\\mathfrak{q}}$ as an extension (as braided Hopf algebras) of $\\mathcal{B}_{\\mathfrak{q}}$ by $\\mathfrak Z_{\\mathfrak{q}}$ where $\\mathfrak Z_{\\mathfrak{q}}$ is isomorphic to the universal envelop"},"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":"1603.09387","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-03-30T21:15:16Z","cross_cats_sorted":[],"title_canon_sha256":"44686624ec65438254ae6de446e6fe16119b33c6dac75ee39d095794f1dfcf78","abstract_canon_sha256":"61a5f5268390fbda2352823f0ce69d17bfbb0848f8794d8f577f58f42e916506"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:58.773755Z","signature_b64":"dVLAkHDEyTG+I8e2QUXoFTVr3luXbc4csrgy4svLFMZMpBcJo2p/G3AXr6+yRKxcMGuNrPKJFLdHiy7h1rWOBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"de07792c2b92cda5c1602b0867aba2c9bcc1b56b311716797a2ca44884d2cca5","last_reissued_at":"2026-05-18T01:17:58.773060Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:58.773060Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A finite-dimensional Lie algebra arising from a Nichols algebra of diagonal type (rank 2)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Fiorela Rossi Bertone, Iv\\'an Angiono, Nicol\\'as Andruskiewitsch","submitted_at":"2016-03-30T21:15:16Z","abstract_excerpt":"Let $\\mathcal{B}_{\\mathfrak{q}}$ be a finite-dimensional Nichols algebra of diagonal type corresponding to a matrix $\\mathfrak{q} \\in \\mathbf{k}^{\\theta \\times \\theta}$, where $\\mathbf{k}$ is an algebraically closed field of characteristic 0. Let $\\mathcal{L}_{\\mathfrak{q}}$ be the Lusztig algebra associated to $\\mathcal{B}_{\\mathfrak{q}}$, see http://arxiv.org/abs/1501.04518. We present $\\mathcal{L}_{\\mathfrak{q}}$ as an extension (as braided Hopf algebras) of $\\mathcal{B}_{\\mathfrak{q}}$ by $\\mathfrak Z_{\\mathfrak{q}}$ where $\\mathfrak Z_{\\mathfrak{q}}$ is isomorphic to the universal envelop"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.09387","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":"1603.09387","created_at":"2026-05-18T01:17:58.773157+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.09387v1","created_at":"2026-05-18T01:17:58.773157+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.09387","created_at":"2026-05-18T01:17:58.773157+00:00"},{"alias_kind":"pith_short_12","alias_value":"3YDXSLBLSLG2","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_16","alias_value":"3YDXSLBLSLG2LQLA","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_8","alias_value":"3YDXSLBL","created_at":"2026-05-18T12:29:58.707656+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/3YDXSLBLSLG2LQLAFMEGPK5CZG","json":"https://pith.science/pith/3YDXSLBLSLG2LQLAFMEGPK5CZG.json","graph_json":"https://pith.science/api/pith-number/3YDXSLBLSLG2LQLAFMEGPK5CZG/graph.json","events_json":"https://pith.science/api/pith-number/3YDXSLBLSLG2LQLAFMEGPK5CZG/events.json","paper":"https://pith.science/paper/3YDXSLBL"},"agent_actions":{"view_html":"https://pith.science/pith/3YDXSLBLSLG2LQLAFMEGPK5CZG","download_json":"https://pith.science/pith/3YDXSLBLSLG2LQLAFMEGPK5CZG.json","view_paper":"https://pith.science/paper/3YDXSLBL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.09387&json=true","fetch_graph":"https://pith.science/api/pith-number/3YDXSLBLSLG2LQLAFMEGPK5CZG/graph.json","fetch_events":"https://pith.science/api/pith-number/3YDXSLBLSLG2LQLAFMEGPK5CZG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3YDXSLBLSLG2LQLAFMEGPK5CZG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3YDXSLBLSLG2LQLAFMEGPK5CZG/action/storage_attestation","attest_author":"https://pith.science/pith/3YDXSLBLSLG2LQLAFMEGPK5CZG/action/author_attestation","sign_citation":"https://pith.science/pith/3YDXSLBLSLG2LQLAFMEGPK5CZG/action/citation_signature","submit_replication":"https://pith.science/pith/3YDXSLBLSLG2LQLAFMEGPK5CZG/action/replication_record"}},"created_at":"2026-05-18T01:17:58.773157+00:00","updated_at":"2026-05-18T01:17:58.773157+00:00"}