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The proof is based on the structure of cells of $\\widetilde{\\mathbf U}$, studied previously in [http://arxiv.org/abs/math/0212253], the author's joint work with Beck. We here give more direct proof based on Lemma 6.17 in [http://arxiv.org/abs/math/0212253], together with a property of the bilinear form introduced in [http://arxiv.org/abs/math/0204183]. We also prove that cell ideals are idempotent, and he"},"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":"1406.1298","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-06-05T08:39:21Z","cross_cats_sorted":[],"title_canon_sha256":"9fc1b688debc404dae0e830f82c038221893f518c8feb820df4251d10dea24a8","abstract_canon_sha256":"6f4ce796528a3be84c13a1bb7a0a4b6748cd6619e8952d0876f037bea11c6edf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:16.972974Z","signature_b64":"VaPA74dXK3kmv5Nv0n1mI0KYNUZnSgOA2/0SjGv/2DSxagkIsoE0injAJiB7EJc3/RK7yzyWqLyXeD3NPzWIAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"62ce07b80a5cced8be486b6d56f1c43d4f5c42d94a96925782e971c5d0e3583a","last_reissued_at":"2026-05-18T02:48:16.972530Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:16.972530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Affine cellularity of quantum affine algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Hiraku Nakajima","submitted_at":"2014-06-05T08:39:21Z","abstract_excerpt":"Cui (arXiv:1405.6441) has shown that the modified quantum affine algebra $\\widetilde{\\mathbf U}$ (more precisely its quotients, BLN algebras) is affine cellular in the sense of Koenig and Xi. 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