{"paper":{"title":"Special bi-invariant linear connections on Lie groups and finite dimensional Poisson structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Mohamed Boucetta, Sa\\\"id Benayadi","submitted_at":"2013-12-07T09:50:19Z","abstract_excerpt":"Let $G$ be a connected Lie group and $\\mathfrak{g}$ its Lie algebra. We denote by $\\nabla^0$ the torsion free bi-invariant linear connection on $G$ given by $\\nabla^0_XY=\\frac12[X,Y],$ for any left invariant vector fields $X,Y$. A Poisson structure on $\\mathfrak{g}$ is a commutative and associative product on $\\mathfrak{g}$ for which $\\mathrm{ad}_u$ is a derivation, for any $u\\in\\mathfrak{g}$.\n  A torsion free bi-invariant linear connections on $G$ which have the same curvature as $\\nabla^0$ is called special. We show that there is a bijection between the space of special connections on $G$ an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2076","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"}