{"paper":{"title":"Analytic Linear Lie rack Structures on Leibniz Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Fatima-Ezzahrae Abid, Hamid Abchir, Mohamed Boucetta","submitted_at":"2019-08-14T10:17:28Z","abstract_excerpt":"A linear Lie rack structure on a finite dimensional vector space $V$ is a Lie rack operation $(x,y)\\mapsto x\\rhd y$ pointed at the origin and such that for any $x$, the left translation $\\mathrm{L}_x:y\\mapsto \\mathrm{L}_x(y)= x\\rhd y$ is linear. A linear Lie rack operation $\\rhd$ is called analytic if for any $x,y\\in V$,\n  \\[ x\\rhd y=y+\\sum_{n=1}^\\infty A_{n,1}(x,\\ldots,x,y), \\]where $A_{n,1}:V\\times\\ldots\\times V\\Leftarrow V$ is an $n+1$-multilinear map symmetric in the $n$ first arguments. In this case, $A_{1,1}$ is exactly the left Leibniz product associated to $\\rhd$. Any left Leibniz alge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.05057","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/1908.05057/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"}