{"paper":{"title":"Versal deformations of a Dirac type differential operator","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anatoliy K. Prykarpatsky, Denis Blackmore","submitted_at":"1999-07-01T00:00:00Z","abstract_excerpt":"If we are given a smooth differential operator in the variable $x\\in {\\mathbb R}/2\\pi {\\mathbb Z},$ its normal form, as is well known, is the simplest form obtainable by means of the $\\mbox{Diff}(S^1)$-group action on the space of all such operators. A versal deformation of this operator is a normal form for some parametric infinitesimal family including the operator. Our study is devoted to analysis of versal deformations of a Dirac type differential operator using the theory of induced $\\mbox{Diff}(S^1)$-actions endowed with centrally extended Lie-Poisson brackets. After constructing a gener"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9907211","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"}