{"paper":{"title":"The center of the generic G-crossed product","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Ofir David","submitted_at":"2014-01-19T18:53:22Z","abstract_excerpt":"Let G be a finite group and let F be a field of characteristic zero. In this paper we construct a generic G-crossed product over F using generic graded matrices. The center of this generic G-crossed product, denoted by F(G), is then the invariant field of a suitable G action on a field of rational functions in several indeterminates. The main goal of this paper is to study the extensions F(G)/F given that F contains enough roots of unity and determine how close they are to being purely transcendental.\n  In particular we show that F(G)/F is a stably rational extension for $G = C_2 \\times C_{2n}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4717","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"}