{"paper":{"title":"Free group algebras in division rings with valuation II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Javier S\\'anchez","submitted_at":"2018-10-29T23:00:33Z","abstract_excerpt":"We apply the filtered and graded methods developed in earlier works to find (noncommutative) free group algebras in division rings.\n  If $L$ is a Lie algebra, we denote by $U(L)$ its universal enveloping algebra. P. M. Cohn constructed a division ring $\\mathfrak{D}_L$ that contains $U(L)$. We denote by $\\mathfrak{D}(L)$ the division subring of $\\mathfrak{D}_L$ generated by $U(L)$.\n  Let $k$ be a field of characteristic zero and $L$ be a nonabelian Lie $k$-algebra. If either $L$ is residually nilpotent or $U(L)$ is an Ore domain, we show that $\\mathfrak{D}(L)$ contains (noncommutative) free gro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12449","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"}