{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NBOQKJI4DN7LL5BU4WLE24JKB3","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":"818244bc37f812f99128a266214f4bb0e9ca44d55e9b34a0b84d0873e9334e45","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-04-16T23:41:18Z","title_canon_sha256":"27f44d6d83c94925fee9c479205ca748c0b1f8f6fb5aa5b9350d112953f37f59"},"schema_version":"1.0","source":{"id":"1404.4402","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.4402","created_at":"2026-05-18T02:49:45Z"},{"alias_kind":"arxiv_version","alias_value":"1404.4402v2","created_at":"2026-05-18T02:49:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4402","created_at":"2026-05-18T02:49:45Z"},{"alias_kind":"pith_short_12","alias_value":"NBOQKJI4DN7L","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NBOQKJI4DN7LL5BU","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NBOQKJI4","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:a972d8603637f10eec586dcf5c1375c0cd4b966a58a38d9da6439e631ade391e","target":"graph","created_at":"2026-05-18T02:49:45Z","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":"In this paper we consider several homological dimensions of crossed products $A _{\\alpha} ^{\\sigma} G$, where $A$ is a left Noetherian ring and $G$ is a finite group. We revisit the induction and restriction functors in derived categories, generalizing a few classical results for separable extensions. The global dimension and finitistic dimension of $A ^{\\sigma} _{\\alpha} G$ are classified: global dimension of $A ^{\\sigma} _{\\alpha} G$ is either infinity or equal to that of $A$, and finitistic dimension of $A ^{\\sigma} _{\\alpha} G$ coincides with that of $A$. A criterion for skew group rings t","authors_text":"Liping Li","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-04-16T23:41:18Z","title":"Homological dimensions of crossed products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4402","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:e72665812e6fcc8179dbba1af51f8c216843ae3c5dc5809f0827a89b81ee9637","target":"record","created_at":"2026-05-18T02:49:45Z","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":"818244bc37f812f99128a266214f4bb0e9ca44d55e9b34a0b84d0873e9334e45","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-04-16T23:41:18Z","title_canon_sha256":"27f44d6d83c94925fee9c479205ca748c0b1f8f6fb5aa5b9350d112953f37f59"},"schema_version":"1.0","source":{"id":"1404.4402","kind":"arxiv","version":2}},"canonical_sha256":"685d05251c1b7eb5f434e5964d712a0ef3664d1b7f60d99564a5e6780b789923","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"685d05251c1b7eb5f434e5964d712a0ef3664d1b7f60d99564a5e6780b789923","first_computed_at":"2026-05-18T02:49:45.490289Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:45.490289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v+jD7gU+Ya8iisdOV+kDU0Wf9vPBUrR3OyQ12cKwwHC8IQYrvaEybCLVXECmHaFWChkGdG6M5PaQ8hOfYvmWDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:45.490639Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.4402","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e72665812e6fcc8179dbba1af51f8c216843ae3c5dc5809f0827a89b81ee9637","sha256:a972d8603637f10eec586dcf5c1375c0cd4b966a58a38d9da6439e631ade391e"],"state_sha256":"4378724b4038322167a1b5f3b0709280567be2646bf92186d1360221f67e26b2"}