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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1312.2076","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-12-07T09:50:19Z","cross_cats_sorted":[],"title_canon_sha256":"18dd84191ff7fd379e5b8269d6e4c57163c39cf2dbfac20d9082e4fb0ccfc3a3","abstract_canon_sha256":"dec08862277cfd1f725e29ba51c5b71432f0616e14721e5b31a9a4b28bd055f2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:17.401669Z","signature_b64":"1eqB9Lk6kfGAVZgd/BHCrf+mZy3ziXCKL2rF3KeLPYt6F8mmiNAAkM9FmUa8WLUQKe5ocJvqG1kDbXPIp9ECBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f5367f3e6135dc2a218e398a1206736eb3a877206c3c244374e5e8fe4352c6b","last_reissued_at":"2026-05-18T03:05:17.401184Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:17.401184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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