{"paper":{"title":"Tangent Lie groups are Riemannian naturally reductive spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ana Cristina Ferreira, Ilka Agricola","submitted_at":"2016-03-20T12:34:15Z","abstract_excerpt":"Given a compact Lie group $G$ with Lie algebra $\\mathfrak{g}$, we consider its tangent Lie group $TG\\cong G\\ltimes_{\\mathrm{Ad}} \\mathfrak{g}$. In this short note, we prove that $TG$ admits a left-invariant naturally reductive Riemannian metric $g$ and a metric connection with skew torsion $\\nabla$ such that $(TG,g,\\nabla)$ is naturally reductive. An alternative spinorial description of the same connection on the direct product $G\\times \\mathfrak{g}$ generalizes in a rather subtle way to $TS^7$, which is in many senses almost a tangent Lie group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06211","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"}