{"paper":{"title":"(Co)Homology of Poset Lie Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.RA"],"primary_cat":"math.AT","authors_text":"Ale\\v{s} Vavpeti\\v{c}, Leon Lampret","submitted_at":"2015-04-29T07:31:40Z","abstract_excerpt":"We investigate the (co)homological properties of two classes of Lie algebras that are constructed from any finite poset: the solvable class $\\frak{gl}^\\preceq$ and the nilpotent class $\\frak{gl}^\\prec$. We confirm the conjecture of Jollenbeck that says: every prime power $p^r\\!\\leq\\!n\\!-\\!2$ appears as torsion in $H_\\ast(\\frak{nil}_n;\\mathbb{Z})$, and every prime power $p^r\\!\\leq\\!n\\!-\\!1$ appears as torsion in $H_\\ast(\\frak{sol}_n;\\mathbb{Z})$. If $\\preceq$ is a bounded poset, then the (co)homology of $\\frak{gl}^\\preceq$ is \\emph{torsion-convex}, i.e. if it contains $p$-torsion, then it also "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.07743","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"}