{"paper":{"title":"From almost (para)-complex structures to affine structures on Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Gabriela P. Ovando, Giovanni Calvaruso","submitted_at":"2016-04-28T14:24:38Z","abstract_excerpt":"Let $G=H\\ltimes K$ denote a semidirect product Lie group with Lie algebra $\\mathfrak g=\\mathfrak h \\oplus \\mathfrak k$, where $\\mathfrak k$ is an ideal and $\\mathfrak h$ is a subalgebra of the same dimension as $\\mathfrak k$. There exist some natural split isomorphisms $S$ with $S^2=\\pm \\,Id$ on $\\mathfrak g$: given any linear isomorphism $j:\\mathfrak h \\to \\mathfrak k$, we have the almost complex structure $J(x,v)=(-j^{-1}v, jx)$ and the almost paracomplex structure $E(x,v)=(j^{-1}v, jx)$. In this work we show that the integrability of the structures $J$ and $E$ above is equivalent to the exi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.08433","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"}