{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:X6B5EWQTCGQPGDFTQDKFU6XDEQ","short_pith_number":"pith:X6B5EWQT","schema_version":"1.0","canonical_sha256":"bf83d25a1311a0f30cb380d45a7ae324368c22752200a7f4ad4cbcbd776fe820","source":{"kind":"arxiv","id":"1606.05424","version":2},"attestation_state":"computed","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 $\\Gamma \\cong \\mathbb{Z}_2$"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1606.05424","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-06-17T06:22:49Z","cross_cats_sorted":[],"title_canon_sha256":"68a9cbb2af7693841458e52914bac321f2808d38b16dddb4eb5cb051a249f9d3","abstract_canon_sha256":"fb554d48b98082fc4ad21a0c1d503741256ec97b0a4b44742882d8f80838310f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:16.335417Z","signature_b64":"B+Sbkox0PY558DaHZP37gPdERZa6dmtRsv0Cd4/5C2HgS1Ped2MID3F1CyNnBjrXJTdFSZzxua4axTttuyODDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf83d25a1311a0f30cb380d45a7ae324368c22752200a7f4ad4cbcbd776fe820","last_reissued_at":"2026-05-18T01:12:16.334965Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:16.334965Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1606.05424","created_at":"2026-05-18T01:12:16.335022+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.05424v2","created_at":"2026-05-18T01:12:16.335022+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.05424","created_at":"2026-05-18T01:12:16.335022+00:00"},{"alias_kind":"pith_short_12","alias_value":"X6B5EWQTCGQP","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_16","alias_value":"X6B5EWQTCGQPGDFT","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_8","alias_value":"X6B5EWQT","created_at":"2026-05-18T12:30:51.357362+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/X6B5EWQTCGQPGDFTQDKFU6XDEQ","json":"https://pith.science/pith/X6B5EWQTCGQPGDFTQDKFU6XDEQ.json","graph_json":"https://pith.science/api/pith-number/X6B5EWQTCGQPGDFTQDKFU6XDEQ/graph.json","events_json":"https://pith.science/api/pith-number/X6B5EWQTCGQPGDFTQDKFU6XDEQ/events.json","paper":"https://pith.science/paper/X6B5EWQT"},"agent_actions":{"view_html":"https://pith.science/pith/X6B5EWQTCGQPGDFTQDKFU6XDEQ","download_json":"https://pith.science/pith/X6B5EWQTCGQPGDFTQDKFU6XDEQ.json","view_paper":"https://pith.science/paper/X6B5EWQT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.05424&json=true","fetch_graph":"https://pith.science/api/pith-number/X6B5EWQTCGQPGDFTQDKFU6XDEQ/graph.json","fetch_events":"https://pith.science/api/pith-number/X6B5EWQTCGQPGDFTQDKFU6XDEQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X6B5EWQTCGQPGDFTQDKFU6XDEQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X6B5EWQTCGQPGDFTQDKFU6XDEQ/action/storage_attestation","attest_author":"https://pith.science/pith/X6B5EWQTCGQPGDFTQDKFU6XDEQ/action/author_attestation","sign_citation":"https://pith.science/pith/X6B5EWQTCGQPGDFTQDKFU6XDEQ/action/citation_signature","submit_replication":"https://pith.science/pith/X6B5EWQTCGQPGDFTQDKFU6XDEQ/action/replication_record"}},"created_at":"2026-05-18T01:12:16.335022+00:00","updated_at":"2026-05-18T01:12:16.335022+00:00"}