{"paper":{"title":"Tube representations and twisting of graded categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.QA","authors_text":"Jyotishman Bhowmick, Makoto Yamashita, Narayan Rakshit, Shamindra Ghosh","submitted_at":"2018-01-05T12:17:22Z","abstract_excerpt":"We study deformation of tube algebra under twisting of graded monoidal categories. When a tensor category $\\mathcal{C}$ is graded over a group $\\Gamma$, a torus-valued 3-cocycle on $\\Gamma$ can be used to deform the associator of $\\mathcal{C}$. Based on a natural Fell bundle structure of the tube algebra over the action groupoid of the adjoint action of $\\Gamma$, we show that the tube algebra of the twisted category is a 2-cocycle twisting of the original one."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.01735","kind":"arxiv","version":2},"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"}