{"paper":{"title":"Circle and line bundles over generalized Weyl algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Tomasz Brzezi\\'nski","submitted_at":"2014-05-13T11:25:26Z","abstract_excerpt":"Strongly $\\mathbb{Z}$-graded algebras or principal circle bundles and associated line bundles or invertible bimodules over a class of generalized Weyl algebras $\\mathcal{B}(p;q, 0)$ (over a ring of polynomials in one variable) are constructed. The Chern-Connes pairing between the cyclic cohomology of $\\mathcal{B}(p;q, 0)$ and the isomorphism classes of sections of associated line bundles over $\\mathcal{B}(p;q, 0)$ is computed thus demonstrating that these bundles, which are labeled by integers, are non-trivial and mutually non-isomorphic. The constructed strongly $\\mathbb{Z}$-graded algebras a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.3105","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"}