{"paper":{"title":"The group of automorphisms of the algebra of polynomial integro-differential operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.AG","authors_text":"V. V. Bavula","submitted_at":"2009-12-13T20:15:05Z","abstract_excerpt":"The group $\\rG_n$ of automorphisms of the algebra $\\mI_n:=K< x_1, >..., x_n, \\frac{\\der}{\\der x_1}, ... ,\\frac{\\der}{\\der x_n}, \\int_1, >..., \\int_n>$ of polynomial integro-differential operators is found: $$ \\rG_n=S_n\\ltimes \\mT^n\\ltimes \\Inn (\\mI_n) \\supseteq\n  S_n\\ltimes \\mT^n \\ltimes \\underbrace{\\GL_\\infty (K)\\ltimes... \\ltimes \\GL_\\infty (K)}_{2^n-1 {\\rm times}}, $$ $$ \\rG_1\\simeq \\mT^1 \\ltimes \\GL_\\infty (K),$$ where $S_n$ is the symmetric group, $\\mT^n$ is the $n$-dimensional torus, $\\Inn (\\mI_n)$ is the group of inner automorphisms of $\\mI_n$ (which is huge). It is proved that each aut"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.2537","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"}