{"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. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1298","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":""},"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"}