{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:APT7WSCOL4YHFTUG7PI2VEJF2V","short_pith_number":"pith:APT7WSCO","schema_version":"1.0","canonical_sha256":"03e7fb484e5f3072ce86fbd1aa9125d571bfd819b9f2d26f6b8330096d61129b","source":{"kind":"arxiv","id":"1802.01357","version":1},"attestation_state":"computed","paper":{"title":"Differential calculus on $\\mathbf{h}$-deformed spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.QA","math.RA","math.RT"],"primary_cat":"math-ph","authors_text":"Basile Herlemont","submitted_at":"2018-02-05T11:43:03Z","abstract_excerpt":"The ring $\\text{Diff}_{\\mathbf{h}}(n)$ of $\\mathbf{h}$-deformed differential operators appears in the theory of reduction algebras. In this thesis, we construct the rings of generalized differential operators on the $\\mathbf{h}$-deformed vector spaces of $\\mathfrak{gl}$-type. In contrast to the $q$-deformed vector spaces for which the ring of differential operators is unique up to an isomorphism, the general ring of $\\mathbf{h}$-deformed differential operators $\\text{Diff}_{\\mathbf{h},\\sigma}(n)$ is labeled by a rational function $\\sigma$ in $n$ variables, satisfying an over-determined system "},"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":"1802.01357","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-02-05T11:43:03Z","cross_cats_sorted":["math.MP","math.QA","math.RA","math.RT"],"title_canon_sha256":"a2e4e5ca7835457f94cb5899d7c681284039c58afa6ea17a387e0e9ee4286444","abstract_canon_sha256":"3b65f9d1f33b8e963f4280350d2f419db2b6c2b8b159f07db014a3d9f720cb8c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:26.617118Z","signature_b64":"K1R7fDOEgb5NqtuP6Hd5K+zfevEki+YI/D+zjgki0YxSOwdgf0kX2F8g7TUHcAJpiZbwfi/LGzEXoqboBiVWDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03e7fb484e5f3072ce86fbd1aa9125d571bfd819b9f2d26f6b8330096d61129b","last_reissued_at":"2026-05-18T00:24:26.616646Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:26.616646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Differential calculus on $\\mathbf{h}$-deformed spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.QA","math.RA","math.RT"],"primary_cat":"math-ph","authors_text":"Basile Herlemont","submitted_at":"2018-02-05T11:43:03Z","abstract_excerpt":"The ring $\\text{Diff}_{\\mathbf{h}}(n)$ of $\\mathbf{h}$-deformed differential operators appears in the theory of reduction algebras. In this thesis, we construct the rings of generalized differential operators on the $\\mathbf{h}$-deformed vector spaces of $\\mathfrak{gl}$-type. In contrast to the $q$-deformed vector spaces for which the ring of differential operators is unique up to an isomorphism, the general ring of $\\mathbf{h}$-deformed differential operators $\\text{Diff}_{\\mathbf{h},\\sigma}(n)$ is labeled by a rational function $\\sigma$ in $n$ variables, satisfying an over-determined system "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.01357","kind":"arxiv","version":1},"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":"1802.01357","created_at":"2026-05-18T00:24:26.616720+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.01357v1","created_at":"2026-05-18T00:24:26.616720+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.01357","created_at":"2026-05-18T00:24:26.616720+00:00"},{"alias_kind":"pith_short_12","alias_value":"APT7WSCOL4YH","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_16","alias_value":"APT7WSCOL4YHFTUG","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_8","alias_value":"APT7WSCO","created_at":"2026-05-18T12:32:13.499390+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/APT7WSCOL4YHFTUG7PI2VEJF2V","json":"https://pith.science/pith/APT7WSCOL4YHFTUG7PI2VEJF2V.json","graph_json":"https://pith.science/api/pith-number/APT7WSCOL4YHFTUG7PI2VEJF2V/graph.json","events_json":"https://pith.science/api/pith-number/APT7WSCOL4YHFTUG7PI2VEJF2V/events.json","paper":"https://pith.science/paper/APT7WSCO"},"agent_actions":{"view_html":"https://pith.science/pith/APT7WSCOL4YHFTUG7PI2VEJF2V","download_json":"https://pith.science/pith/APT7WSCOL4YHFTUG7PI2VEJF2V.json","view_paper":"https://pith.science/paper/APT7WSCO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.01357&json=true","fetch_graph":"https://pith.science/api/pith-number/APT7WSCOL4YHFTUG7PI2VEJF2V/graph.json","fetch_events":"https://pith.science/api/pith-number/APT7WSCOL4YHFTUG7PI2VEJF2V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/APT7WSCOL4YHFTUG7PI2VEJF2V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/APT7WSCOL4YHFTUG7PI2VEJF2V/action/storage_attestation","attest_author":"https://pith.science/pith/APT7WSCOL4YHFTUG7PI2VEJF2V/action/author_attestation","sign_citation":"https://pith.science/pith/APT7WSCOL4YHFTUG7PI2VEJF2V/action/citation_signature","submit_replication":"https://pith.science/pith/APT7WSCOL4YHFTUG7PI2VEJF2V/action/replication_record"}},"created_at":"2026-05-18T00:24:26.616720+00:00","updated_at":"2026-05-18T00:24:26.616720+00:00"}