{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:SQ4GJ6AIN3AXSWFO5TCRZKYPYS","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":"11c0481a7c7de0b3183ed99f781f611c92877943c9bb52d07feb7a22efb9ce36","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2011-09-13T13:04:04Z","title_canon_sha256":"56c17802ae3d313e9235dfe77f257398c944614a4da8db73e2189fce37d4f0b9"},"schema_version":"1.0","source":{"id":"1109.2770","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.2770","created_at":"2026-05-18T03:54:49Z"},{"alias_kind":"arxiv_version","alias_value":"1109.2770v1","created_at":"2026-05-18T03:54:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.2770","created_at":"2026-05-18T03:54:49Z"},{"alias_kind":"pith_short_12","alias_value":"SQ4GJ6AIN3AX","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SQ4GJ6AIN3AXSWFO","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SQ4GJ6AI","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:d30797040903d0dd886d4c68eaf34e4bc46326a76444c92895f0a3a1f2692085","target":"graph","created_at":"2026-05-18T03:54:49Z","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 k be an algebraically closed field of characteristic p> 0. For a basic classical Lie superalgebra, we show its restricted cohomology algebra is a finitely generated algebra. Thus the cohomological support theory can be established. As a consequence, we show that the restricted enveloping algebra of a basic classical Lie superalgebra g is always wild except g=sl(2) or g=osp(1|2) or g=C(2). Moreover, all finite dimensional indecomposable restricted representations of u(osp(1|2)), the restricted enveloping algebra of Lie superalgebra osp(1|2), are determined.","authors_text":"Gongxiang Liu","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2011-09-13T13:04:04Z","title":"Support varieties and representations of tame basic classical Lie superalgebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2770","kind":"arxiv","version":1},"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":"sha256:70647c0ab94b4cdedf880011558a4a79a9f4df303858bdb79460a0823c1f412a","target":"record","created_at":"2026-05-18T03:54:49Z","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":"11c0481a7c7de0b3183ed99f781f611c92877943c9bb52d07feb7a22efb9ce36","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2011-09-13T13:04:04Z","title_canon_sha256":"56c17802ae3d313e9235dfe77f257398c944614a4da8db73e2189fce37d4f0b9"},"schema_version":"1.0","source":{"id":"1109.2770","kind":"arxiv","version":1}},"canonical_sha256":"943864f8086ec17958aeecc51cab0fc48ed028954666b9e4f375741ecefc256d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"943864f8086ec17958aeecc51cab0fc48ed028954666b9e4f375741ecefc256d","first_computed_at":"2026-05-18T03:54:49.339012Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:49.339012Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5kjC2HZVhtbTKly8i2m4LUCxKbJmOPLdK/uCkqwRTTMd6KSu1oJ4atylwUzmejT3boNoQ5fApP5av8NBbIOAAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:49.339747Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.2770","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:70647c0ab94b4cdedf880011558a4a79a9f4df303858bdb79460a0823c1f412a","sha256:d30797040903d0dd886d4c68eaf34e4bc46326a76444c92895f0a3a1f2692085"],"state_sha256":"760b434d75d880ea79a2a736d112f17a418306dcf85d16638558fa51915843b7"}