{"paper":{"title":"Extensions of the Frobenius to ring of differential operators on polynomial algebra in prime characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.AG"],"primary_cat":"math.RA","authors_text":"V. V. Bavula","submitted_at":"2008-04-07T17:39:05Z","abstract_excerpt":"Let $K$ be a field of characteristic $p>0$. It is proved that each automorphism $\\s \\in \\Aut_K(\\CDPn)$ of the ring $\\CDPn$ of differential operators on a polynomial algebra $P_n= K[x_1, ..., x_n]$ is {\\em uniquely} determined by the elements $\\s (x_1), ... ,\\s (x_n)$, and the set $\\Frob (\\CDPn)$ of all the extensions of the Frobenius from certain maximal commutative polynomial subalgebras of $\\CDPn$, like $P_n$, is equal to $\\Aut_K(\\CDPn) \\cdot \\CF$ where $\\CF$ is the set of all the extensions of the Frobenius from $P_n$ to $\\CDPn$ that leave invariant the subalgebra of scalar differential ope"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0804.1091","kind":"arxiv","version":2},"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"}