{"paper":{"title":"$A_{\\infty}$-modules and Calogero-Moser Spaces","license":"","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Oleg Chalykh, Yuri Berest","submitted_at":"2004-10-06T23:38:48Z","abstract_excerpt":"We re-examine the bijective correspondence between the set of isomorphism classes of ideals of the first Weyl algebra and associated quiver varieties (Calogero-Moser spaces) \\cite{BW1, BW2}. We give a new explicit construction of this correspondence based on the notion of $\\A$-envelope of a rank one torsion-free $A_1$-module. Though perhaps less geometric than other methods, our approach is much simpler and seems more natural from the point of view of deformation theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0410194","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"}