{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:63A425X6EQLHKBIMUTMNRA6UXV","short_pith_number":"pith:63A425X6","schema_version":"1.0","canonical_sha256":"f6c1cd76fe241675050ca4d8d883d4bd4106e1eb3740568b8775a9fe1b0ac361","source":{"kind":"arxiv","id":"0810.0851","version":2},"attestation_state":"computed","paper":{"title":"On the Topology of Kac-Moody groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Nitu Kitchloo","submitted_at":"2008-10-05T20:32:09Z","abstract_excerpt":"We study the topology of spaces related to Kac-Moody groups. Given a split Kac-Moody group over the complex numbers, let K denote the unitary form with maximal torus T having normalizer N(T). In this article we study the cohomology of the flag manifold K/T, as a module over the Nil-Hecke ring, as well as the (co)homology of K as a Hopf algebra. In particular, if F is a field of positive characteristic, we show that H_*(K,F) is a finitely generated algebra, and that H^*(K,F) is finitely generated only if K is a compact Lie group . We also study the stable homotopy type of the classifying space "},"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":"0810.0851","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2008-10-05T20:32:09Z","cross_cats_sorted":[],"title_canon_sha256":"64fa9b09316a26cb15a2adf178cc6342266f34904f76347e70dca40b13a60b5e","abstract_canon_sha256":"3f4d2e3021c7f2f6d9a07a426adcd689f5524d31895bcb08d0512a82fc5b693a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:29.268876Z","signature_b64":"0sWfGbvD+JcM8Eby10u3o+cTj+fkwlPca8KFQLVaFN4e3botIf0uMW9KDlTB90fUOzQFBU/H7fweDUB+PSrXDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6c1cd76fe241675050ca4d8d883d4bd4106e1eb3740568b8775a9fe1b0ac361","last_reissued_at":"2026-05-18T03:37:29.268105Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:29.268105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Topology of Kac-Moody groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Nitu Kitchloo","submitted_at":"2008-10-05T20:32:09Z","abstract_excerpt":"We study the topology of spaces related to Kac-Moody groups. Given a split Kac-Moody group over the complex numbers, let K denote the unitary form with maximal torus T having normalizer N(T). In this article we study the cohomology of the flag manifold K/T, as a module over the Nil-Hecke ring, as well as the (co)homology of K as a Hopf algebra. In particular, if F is a field of positive characteristic, we show that H_*(K,F) is a finitely generated algebra, and that H^*(K,F) is finitely generated only if K is a compact Lie group . We also study the stable homotopy type of the classifying space "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.0851","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":"0810.0851","created_at":"2026-05-18T03:37:29.268246+00:00"},{"alias_kind":"arxiv_version","alias_value":"0810.0851v2","created_at":"2026-05-18T03:37:29.268246+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.0851","created_at":"2026-05-18T03:37:29.268246+00:00"},{"alias_kind":"pith_short_12","alias_value":"63A425X6EQLH","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_16","alias_value":"63A425X6EQLHKBIM","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_8","alias_value":"63A425X6","created_at":"2026-05-18T12:25:56.245647+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/63A425X6EQLHKBIMUTMNRA6UXV","json":"https://pith.science/pith/63A425X6EQLHKBIMUTMNRA6UXV.json","graph_json":"https://pith.science/api/pith-number/63A425X6EQLHKBIMUTMNRA6UXV/graph.json","events_json":"https://pith.science/api/pith-number/63A425X6EQLHKBIMUTMNRA6UXV/events.json","paper":"https://pith.science/paper/63A425X6"},"agent_actions":{"view_html":"https://pith.science/pith/63A425X6EQLHKBIMUTMNRA6UXV","download_json":"https://pith.science/pith/63A425X6EQLHKBIMUTMNRA6UXV.json","view_paper":"https://pith.science/paper/63A425X6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0810.0851&json=true","fetch_graph":"https://pith.science/api/pith-number/63A425X6EQLHKBIMUTMNRA6UXV/graph.json","fetch_events":"https://pith.science/api/pith-number/63A425X6EQLHKBIMUTMNRA6UXV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/63A425X6EQLHKBIMUTMNRA6UXV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/63A425X6EQLHKBIMUTMNRA6UXV/action/storage_attestation","attest_author":"https://pith.science/pith/63A425X6EQLHKBIMUTMNRA6UXV/action/author_attestation","sign_citation":"https://pith.science/pith/63A425X6EQLHKBIMUTMNRA6UXV/action/citation_signature","submit_replication":"https://pith.science/pith/63A425X6EQLHKBIMUTMNRA6UXV/action/replication_record"}},"created_at":"2026-05-18T03:37:29.268246+00:00","updated_at":"2026-05-18T03:37:29.268246+00:00"}