{"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"}