{"paper":{"title":"Matched Pair Analysis of Euler-Poincar\\'{e} Flow on Hamiltonian Vector Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Cristina Sard\\'on, Marcin Zajac, O\\u{g}ul Esen","submitted_at":"2021-03-07T17:10:46Z","abstract_excerpt":"In this paper we provide a matched pair decomposition of the space of symmetric contravariant tensors $\\mathfrak{T}\\mathcal{Q}$. From this procedure two complementary Lie subalgebras of $\\mathfrak{T}\\mathcal{Q}$ under \\textit{mutual} interaction arise. Introducing a lift operator, the matched pair decomposition of the space of Hamiltonian vector fields is determined. According to these realizations, Euler-Poincar\\'{e} flows on such spaces are decomposed into two subdynamics: one of which is the Euler--Poincar\\'{e} formulation of isentropic fluid flows, and the other one corresponds with Euler-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.04401","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2103.04401/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}