{"paper":{"title":"Automorphisms and Ideals of Noncommutative Deformations of $\\mathbb{C}^2/\\mathbb{Z}_2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Alimjon Eshmatov, Farkhod Eshmatov, Vyacheslav Futorny, Xiaojun Chen","submitted_at":"2016-06-17T06:22:49Z","abstract_excerpt":"Let $O_\\tau(\\Gamma)$ be a family of algebras \\textit{quantizing} the coordinate ring of $\\mathbb{C}^2 / \\Gamma$, where $\\Gamma$ is a finite subgroup of $\\mathrm{SL}_2(\\mathbb{C})$, and let $G_{\\Gamma}$ be the automorphism group of $O_\\tau$. We study the natural action of $G_\\Gamma$ on the space of right ideals of $O_\\tau$ (equivalently, finitely generated rank $1$ projective $O_\\tau$-modules). It is known that the later can be identified with disjoint union of algebraic (quiver) varieties, and this identification is $G_\\Gamma$-equivariant. In the present paper, when $\\Gamma \\cong \\mathbb{Z}_2$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.05424","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"}