{"paper":{"title":"Poisson Geometry Related to Atiyah Sequences","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Anatol Odzijewicz, Aneta Sli\\.zewska, Kirill Mackenzie","submitted_at":"2015-06-10T08:49:08Z","abstract_excerpt":"We construct and investigate a short exact sequence of Poisson $\\mathcal{VB}$-groupoids which is canonically related to the Atiyah sequence of a $G$-principal bundle $P$. Our results include a description of the structure of the symplectic leaves of the Poisson groupoid $\\frac{T^*P\\times T^*P}{G}\\rightrightarrows \\frac{T^*P}{G}$. The semidirect product case, which is important for applications in Hamiltonian mechanics, is also discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03216","kind":"arxiv","version":2},"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"}