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We calculate the restricted Lie algebra structure of the first Hochschild cohomology $\\mathcal{L}:={\\rm H}^1(\\mathscr{B}_0(\\mathcal{G}),\\mathscr{B}_0(\\mathcal{G}))$ whenever $\\mathscr{B}_0(\\mathcal{G})$ has finite representation type. As a consequence, we prove that the complexity of the trivial $\\mathcal{G}$-module $k$ coincides with the maximal"},"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":"1907.04093","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-07-09T11:42:49Z","cross_cats_sorted":[],"title_canon_sha256":"aebe6e152db9953b673f4ae6d8cebc7cf5b714aff01cc872a5600743528c0a08","abstract_canon_sha256":"f0367e5cf4f905153ec404cfe553203c7c3fcc178b0da82820c8853c4401d597"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:03.343427Z","signature_b64":"9NjcWKoV2I3/tjnpbRGAfY4NZSABDDAAua45ns019fn72QndzrCqj/kPj0dstWOMiXlX/O4dpKpL0P3OCF6tDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a3c9ea5d78c1ccbf07c0581a2120b48c4c5522b3459b4bd4ec74422afee53a1","last_reissued_at":"2026-05-17T23:41:03.342706Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:03.342706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the first Hochschild cohomology of cocommutative Hopf algebras of finite representation type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Hao Chang","submitted_at":"2019-07-09T11:42:49Z","abstract_excerpt":"Let $\\mathscr{B}_0(\\mathcal{G})\\subseteq k\\mathcal{G}$ be the principal block algebra of the group algebra $k\\mathcal{G}$ of an infinitesimal group scheme $\\mathcal{G}$ over an algebraically closed field $k$ of characteristic ${\\rm char}(k)=:p\\geq 3$. We calculate the restricted Lie algebra structure of the first Hochschild cohomology $\\mathcal{L}:={\\rm H}^1(\\mathscr{B}_0(\\mathcal{G}),\\mathscr{B}_0(\\mathcal{G}))$ whenever $\\mathscr{B}_0(\\mathcal{G})$ has finite representation type. As a consequence, we prove that the complexity of the trivial $\\mathcal{G}$-module $k$ coincides with the maximal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.04093","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":"1907.04093","created_at":"2026-05-17T23:41:03.342831+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.04093v1","created_at":"2026-05-17T23:41:03.342831+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.04093","created_at":"2026-05-17T23:41:03.342831+00:00"},{"alias_kind":"pith_short_12","alias_value":"JI6J5JOXRQOM","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_16","alias_value":"JI6J5JOXRQOMX4D4","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_8","alias_value":"JI6J5JOX","created_at":"2026-05-18T12:33:21.387695+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/JI6J5JOXRQOMX4D4AWA2EEQLJD","json":"https://pith.science/pith/JI6J5JOXRQOMX4D4AWA2EEQLJD.json","graph_json":"https://pith.science/api/pith-number/JI6J5JOXRQOMX4D4AWA2EEQLJD/graph.json","events_json":"https://pith.science/api/pith-number/JI6J5JOXRQOMX4D4AWA2EEQLJD/events.json","paper":"https://pith.science/paper/JI6J5JOX"},"agent_actions":{"view_html":"https://pith.science/pith/JI6J5JOXRQOMX4D4AWA2EEQLJD","download_json":"https://pith.science/pith/JI6J5JOXRQOMX4D4AWA2EEQLJD.json","view_paper":"https://pith.science/paper/JI6J5JOX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.04093&json=true","fetch_graph":"https://pith.science/api/pith-number/JI6J5JOXRQOMX4D4AWA2EEQLJD/graph.json","fetch_events":"https://pith.science/api/pith-number/JI6J5JOXRQOMX4D4AWA2EEQLJD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JI6J5JOXRQOMX4D4AWA2EEQLJD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JI6J5JOXRQOMX4D4AWA2EEQLJD/action/storage_attestation","attest_author":"https://pith.science/pith/JI6J5JOXRQOMX4D4AWA2EEQLJD/action/author_attestation","sign_citation":"https://pith.science/pith/JI6J5JOXRQOMX4D4AWA2EEQLJD/action/citation_signature","submit_replication":"https://pith.science/pith/JI6J5JOXRQOMX4D4AWA2EEQLJD/action/replication_record"}},"created_at":"2026-05-17T23:41:03.342831+00:00","updated_at":"2026-05-17T23:41:03.342831+00:00"}