{"paper":{"title":"Universal Cartan-Lie algebroid of an anchored bundle with connection and compatible geometries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alexei Kotov, Thomas Strobl","submitted_at":"2019-04-11T16:10:33Z","abstract_excerpt":"Consider an anchored bundle $(E,\\rho)$, i.e. a vector bundle $E\\to M$ equipped with a bundle map $\\rho \\colon E \\to TM$ covering the identity. M.~Kapranov showed in the context of Lie-Rinehard algebras that there exists an extension of this anchored bundle to an infinite rank universal free Lie algebroid $FR(E)\\supset E$. We adapt his construction to the case of an anchored bundle equipped with an arbitrary connection, $(E,\\nabla)$, and show that it gives rise to a unique connection $\\tilde \\nabla$ on $FR(E)$ which is compatible with its Lie algebroid structure, thus turning $(FR(E), \\tilde \\n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.05809","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"}