{"paper":{"title":"Formal Verlinde Module","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.SG"],"primary_cat":"math.DG","authors_text":"Yanli Song","submitted_at":"2014-04-18T18:20:43Z","abstract_excerpt":"Let G be a compact, simple and simply connected Lie group and $\\A$ be an equivariant Dixmier-Douady bundle over G. For any fixed level k, we can define a G-C*-algebra $C_{\\A^{k+h}}(G)$ as all the continuous sections of the tensor power $\\A^{k+h}$ vanishing at infinity. A deep theorem by Freed-Hopkins-Teleman showed that the twisted K-homology $KK^{G}(C_{\\A^{k+h}}(G), \\C)$ is isomorphic to the level k Verlinde ring R_{k}(G). By the construction of crossed product, we define a C*-algebra $C^{*}(G,C_{\\A^{k+h}}(G))$. We show that the K-homology KK(C^{*}(G,C_{\\A^{k+h}}(G)),\\C) is isomorphic to the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4850","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"}