{"paper":{"title":"Restricted One-dimensional Central Extensions of the Restricted Filiform Lie Algebras ${\\frak m}_0^\\lambda(p)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Alice Fialowski, Tyler J. Evans","submitted_at":"2018-01-24T20:41:45Z","abstract_excerpt":"We show, for a field ${\\mathbb F}$ of prime characteristic $p>0$, that the truncated filiform Lie algebra ${\\frak m}_0(p)$ admits a family ${\\frak m}_0^\\lambda(p)$ of restricted Lie algebra structures parameterized by elements $\\lambda\\in {\\mathbb F}^p$. We compute the ordinary cohomology groups $H^q({\\frak m}_0^\\lambda(p))$ and restricted cohomology groups $H^q_*({\\frak m}_0^\\lambda(p))$ for $q=1, 2$, and we give explicit descriptions of bases for these cohomology spaces. We apply our results to restricted one-dimensional central Extensions of the algebras ${\\frak m}_0^\\lambda(p)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08178","kind":"arxiv","version":3},"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"}