{"paper":{"title":"Graphs and Metric 2-step Nilpotent Lie Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Lisa DeMeyer, Meera Mainkar, Rachelle DeCoste","submitted_at":"2015-12-25T02:25:29Z","abstract_excerpt":"Dani and Mainkar introduced a method for constructing a 2-step nilpotent Lie algebra $\\mathfrak{n}_G$ from a simple directed graph $G$ in 2005. There is a natural inner product on $\\mathfrak{n}_G$ arising from the construction. We study geometric properties of the associated simply connected 2-step nilpotent Lie group $N$ with Lie algebra $\\mathfrak{n}_G$. We classify singularity properties of the Lie algebra $\\mathfrak{n}_G$ in terms of the graph $G$. A comprehensive description is given of graphs $G$ which give rise to Heisenberg-like Lie algebras. Conditions are given on the graph $G$ and o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07944","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"}