{"paper":{"title":"Weitzenb\\\"ock derivations of nilpotency 3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.RA","authors_text":"David L. Wehlau","submitted_at":"2010-11-01T21:48:16Z","abstract_excerpt":"We consider a Weitzenb\\\"ock derivation $\\Delta$ acting on a polynomial ring $R=K[\\xi_1,\\xi_2,...,\\xi_m]$ over a field $K$ of characteristic 0. The $K$-algebra $R^\\Delta = \\{h \\in R \\mid \\Delta(h) = 0\\}$ is called the algebra of constants. Nowicki considered the case where the Jordan matrix for $\\Delta$ acting on $R_1$, the degree 1 component of $R$, has only Jordan blocks of size 2. He conjectured (\\cite{N}) that a certain set generates $R^{\\Delta}$ in that case. Recently Koury (\\cite{Kh}), Drensky and Makar-Limanov (\\cite{DM}) and Kuroda (\\cite{K}) have given proofs of Nowicki's conjecture. H"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.0454","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"}