{"paper":{"title":"Natural lifts of Dorfman brackets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Charlotte Kirchhoff-Lukat, Madeleine Jotz Lean","submitted_at":"2016-10-19T12:44:12Z","abstract_excerpt":"In this note we prove that, for a vector bundle $E$ over a manifold $M$, a Dorfman bracket on $TM\\oplus E^*$ anchored by $\\operatorname{pr}_{TM}$ and with $E$ a vector bundle over $M$, is equivalent to a lift from $\\Gamma(TM\\oplus E^*)$ to linear sections of $TE\\oplus T^*E\\to E$, that intertwines the given Dorfman bracket with the Courant-Dorfman bracket on sections of $TE\\oplus T^*E$. This shows a universality of the Courant-Dorfman bracket, and allows us to caracterise twistings and symmetries of transitive Dorfman brackets via the corresponding lifts."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05986","kind":"arxiv","version":3},"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"}