{"paper":{"title":"Mixed Commuting Varieties over simple Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.RT","authors_text":"Nham V. Ngo","submitted_at":"2013-01-12T19:55:28Z","abstract_excerpt":"Let $\\mathfrak{g}$ be a simple Lie algebra defined over an algebraically closed field $k$ of characteristic $p$. Fix an integer $r>1$ and suppose that $V_1,\\ldots,V_r$ are irreducible closed subvarieties of $\\mathfrak{g}$. Let $C(V_1,\\ldots,V_r)$ be the closed variety of all the pairwise commuting elements in $V_1\\times\\cdots\\times V_r$. This paper studies the dimension and irreducibility of such varieties with various $V_i$ in a Lie algebra $\\mathfrak{g}$. In particular, we complete the problem for the case when $V_i$'s are either $\\overline{\\mathcal{O}_{\\text{sub}}}$ the closure of the subre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2712","kind":"arxiv","version":4},"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"}