{"paper":{"title":"Minimal Faithful Representation of the Heisenberg Lie Algebra with Abelian Factor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Nadina Elizabeth Rojas","submitted_at":"2012-06-26T00:55:42Z","abstract_excerpt":"For a finite dimensional Lie algebra $\\g$ over a field $\\k$ of characteristic zero, the $\\mu$-function (respectively $\\mu_{nil}$-function) is defined to be the minimal dimension of $V$ such that $\\g$ admits a faithful representation (respectively a faithful nilrepresentation) on $V$. Let $\\h_m$ be the Heisenberg Lie algebra of dimension $2m + 1$ and let $\\mathfrak{a}_n$ be the abelian Lie algebra of dimension $n$. The aim of this paper is to compute $\\mu(\\h_m \\oplus \\mathfrak{a}_n)$ and $\\mu_{nil}(\\h_m \\oplus \\mathfrak{a}_n)$ for all $m,n \\in \\mathbb{N}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5867","kind":"arxiv","version":2},"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"}