{"paper":{"title":"Complete and vertical lifts of Poisson vector fields and infinitesimal deformations of Poisson tensor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Alina Dobrogowska, Grzegorz Jakimowicz, Karolina Wojciechowicz","submitted_at":"2018-07-05T12:25:27Z","abstract_excerpt":"In this paper we prove that both complete and vertical lifts of a Poisson vector field from a Poisson manifold $(M, \\pi)$ to its tangent bundle $(TM, \\pi_{TM})$ are also Poisson. We use this fact to describe the infinitesimal deformations of Poisson tensor $\\pi_{TM}$. We study some of their properties and present a extensive set of examples in a low dimensional case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.01959","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"}