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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0912.2537","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-12-13T20:15:05Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"0326596f5af66ea983d317bf8bbb4103b9c0323c67b87c3bcc1b9e2bebd708d4","abstract_canon_sha256":"75711749a035124118397cdedef5d58e39aacebc6ce5332fb4a2830ee02c4b15"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:35:57.148740Z","signature_b64":"NqUiwyLh9TQ8EeFb/2G7Ov4VYcoaTNeoL+gb5XyzPT5pEm6sWU16cXSuN386Z/4pPFXcxyAivoD6Mfyv7QqMAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a477e545b305285c831193a3ac9cce00c7788f690f3d484556d9e6b26023dcb8","last_reissued_at":"2026-05-18T04:35:57.147708Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:35:57.147708Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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). 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