{"paper":{"title":"The monoidal center and the character algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.QA","authors_text":"Kenichi Shimizu (Shibaura Institute of Technology)","submitted_at":"2015-04-06T00:43:59Z","abstract_excerpt":"For a pivotal finite tensor category $\\mathcal{C}$ over an algebraically closed field $k$, we define the algebra $\\mathsf{CF}(\\mathcal{C})$ of class functions and the internal character $\\mathsf{ch}(X) \\in \\mathsf{CF}(\\mathcal{C})$ for an object $X \\in \\mathcal{C}$ by using an adjunction between $\\mathcal{C}$ and its monoidal center $\\mathcal{Z}(\\mathcal{C})$. We also develop the integral theory in a unimodular finite tensor category by using the same adjunction. By utilizing these tools, we extend some results in the character theory of finite-dimensional Hopf algebras to this category-theore"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01178","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"}