{"paper":{"title":"The algebra of polynomial integro-differential operators is a holonomic bimodule over the subalgebra of polynomial differential operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"V. V. Bavula","submitted_at":"2011-04-03T19:56:00Z","abstract_excerpt":"In contrast to its subalgebra $A_n:=K<x_1, ..., x_n, \\frac{\\der}{\\der x_1}, ...,\\frac{\\der}{\\der x_n}>$ of polynomial differential operators (i.e. the $n$'th Weyl algebra), 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 neither left nor right Noetherian algebra; moreover it contains infinite direct sums of nonzero left and right ideals. It is proved that $\\mI_n$ is a left (right) coherent algebra iff $n=1$; the algebra $\\mI_n$ is a {\\em holonomic $A_n$-bimodule} of length $3^n$ and has"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0423","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"}