{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:X6B5EWQTCGQPGDFTQDKFU6XDEQ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"fb554d48b98082fc4ad21a0c1d503741256ec97b0a4b44742882d8f80838310f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-06-17T06:22:49Z","title_canon_sha256":"68a9cbb2af7693841458e52914bac321f2808d38b16dddb4eb5cb051a249f9d3"},"schema_version":"1.0","source":{"id":"1606.05424","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.05424","created_at":"2026-05-18T01:12:16Z"},{"alias_kind":"arxiv_version","alias_value":"1606.05424v2","created_at":"2026-05-18T01:12:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.05424","created_at":"2026-05-18T01:12:16Z"},{"alias_kind":"pith_short_12","alias_value":"X6B5EWQTCGQP","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"X6B5EWQTCGQPGDFT","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"X6B5EWQT","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:054b92931d047af0a5be35b602eefe1f6eb092ba482c9f6f7f6a935aa23aa847","target":"graph","created_at":"2026-05-18T01:12:16Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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 $\\Gamma \\cong \\mathbb{Z}_2$","authors_text":"Alimjon Eshmatov, Farkhod Eshmatov, Vyacheslav Futorny, Xiaojun Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-06-17T06:22:49Z","title":"Automorphisms and Ideals of Noncommutative Deformations of $\\mathbb{C}^2/\\mathbb{Z}_2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.05424","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b02e9ef18257fc770a3ed605caa390e16ff4eccba55d7ff9c73e382f2ed26ab1","target":"record","created_at":"2026-05-18T01:12:16Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"fb554d48b98082fc4ad21a0c1d503741256ec97b0a4b44742882d8f80838310f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-06-17T06:22:49Z","title_canon_sha256":"68a9cbb2af7693841458e52914bac321f2808d38b16dddb4eb5cb051a249f9d3"},"schema_version":"1.0","source":{"id":"1606.05424","kind":"arxiv","version":2}},"canonical_sha256":"bf83d25a1311a0f30cb380d45a7ae324368c22752200a7f4ad4cbcbd776fe820","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf83d25a1311a0f30cb380d45a7ae324368c22752200a7f4ad4cbcbd776fe820","first_computed_at":"2026-05-18T01:12:16.334965Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:16.334965Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B+Sbkox0PY558DaHZP37gPdERZa6dmtRsv0Cd4/5C2HgS1Ped2MID3F1CyNnBjrXJTdFSZzxua4axTttuyODDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:16.335417Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.05424","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b02e9ef18257fc770a3ed605caa390e16ff4eccba55d7ff9c73e382f2ed26ab1","sha256:054b92931d047af0a5be35b602eefe1f6eb092ba482c9f6f7f6a935aa23aa847"],"state_sha256":"1e93b13cbebcf2bdef3079e9986186ef6a251016ea64214c091efb8a85d37e15"}