{"paper":{"title":"Regular derivations of truncated polynomial rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"Alexander Premet","submitted_at":"2014-05-10T12:16:32Z","abstract_excerpt":"Let $\\Bbbk$ be an algebraically closed field of characteristic $p>2$. Let $\\mathcal{O}_n=\\Bbbk[X_1,\\ldots,X_n]/(X_1^p,\\ldots, X_n^p)$, a truncated polynomial ring in $n$ variables, and denote by $\\mathcal{L}$ the derivation algebra of $\\mathcal{O}_n$. It is known that the ring of all polynomial functions on $\\mathcal{L}$ invariant under the action of the group of $\\mathrm{Aut}(\\mathcal{L})$ is freely generated by $n$ elements. Furthermore, the related quotient morphism is faithfully flat and all its fibres are irreducible complete intersections. An element $x\\in\\mathcal{L}$ is called ${\\it reg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2426","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"}