{"paper":{"title":"The Picard group of the graded module category of a generalized Weyl algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Robert Won","submitted_at":"2016-06-24T19:47:09Z","abstract_excerpt":"The first Weyl algebra, $A_1 = k \\langle x, y\\rangle/(xy-yx - 1)$ is naturally $\\mathbb{Z}$-graded by letting $\\operatorname{deg} x = 1$ and $\\operatorname{deg} y = -1$. Sue Sierra studied $\\operatorname{gr}- A_1$, category of graded right $A_1$-modules, computing its Picard group and classifying all rings graded equivalent to $A_1$. In this paper, we generalize these results by studying the graded module category of certain generalized Weyl algebras. We show that for a generalized Weyl algebra $A(f)$ with base ring $k[z]$ defined by a quadratic polynomial $f$, the Picard group of $\\operatorna"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07799","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"}