{"paper":{"title":"Free Actions on C*-algebra Suspensions and Joins by Finite Cyclic Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN","math.QA"],"primary_cat":"math.OA","authors_text":"Benjamin Passer","submitted_at":"2015-10-14T14:02:02Z","abstract_excerpt":"We present a proof for certain cases of the noncommutative Borsuk-Ulam conjectures proposed by Baum, D\\k{a}browski, and Hajac. When a unital $C^*$-algebra $A$ admits a free action of $\\mathbb{Z}/k\\mathbb{Z}$, $k \\geq 2$, there is no equivariant map from $A$ to the $C^*$-algebraic join of $A$ and the compact \"quantum\" group $C(\\mathbb{Z}/k\\mathbb{Z})$. This also resolves D\\k{a}browski's conjecture on unreduced suspensions of $C^*$-algebras. Finally, we formulate a different type of noncommutative join than the previous authors, which leads to additional open problems for finite cyclic group act"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04100","kind":"arxiv","version":4},"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"}