{"paper":{"title":"A Note on the Automorphism Group of the Bielawski-Pidstrygach Quiver","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.MP","math.SG"],"primary_cat":"math-ph","authors_text":"Alberto Tacchella, Igor Mencattini","submitted_at":"2012-08-17T15:12:02Z","abstract_excerpt":"We show that there exists a morphism between a group $\\Gamma^{\\mathrm{alg}}$ introduced by G. Wilson and a quotient of the group of tame symplectic automorphisms of the path algebra of a quiver introduced by Bielawski and Pidstrygach. The latter is known to act transitively on the phase space $\\mathcal{C}_{n,2}$ of the Gibbons-Hermsen integrable system of rank 2, and we prove that the subgroup generated by the image of $\\Gamma^{\\mathrm{alg}}$ together with a particular tame symplectic automorphism has the property that, for every pair of points of the regular and semisimple locus of $\\mathcal{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3613","kind":"arxiv","version":3},"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"}