{"paper":{"title":"On multilinear operators commuting with Lie derivatives","license":"","headline":"","cross_cats":["math.DG"],"primary_cat":"dg-ga","authors_text":"Andreas Cap, Jan Slovak","submitted_at":"1994-09-28T13:16:35Z","abstract_excerpt":"Let $E_1,\\dots ,E_k$ and $E$ be natural vector bundles defined over the category $\\Cal Mf_m^+$ of smooth oriented $m$--dimensional manifolds and orientation preserving local diffeomorphisms, with $m\\geq 2$. Let $M$ be an object of $\\Cal Mf_m^+$ which is connected. We give a complete classification of all separately continuous $k$--linear operators $D\\:\\Ga _c(E_1M)\\x\\dots\\x\\Ga_c(E_kM)\\to \\Ga (EM)$ defined on sections with compact supports, which commute with Lie derivatives, i\\.e\\. which satisfy $$ \\Cal L_X(D(s_1,\\dots ,s_k))=\\sum _{i=1}^kD(s_1,\\dots ,\\Cal L_Xs_i,\\dots,s_k), $$ for all vector f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"dg-ga/9409005","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"}