{"paper":{"title":"A solution of the problem of standard compact Clifford-Klein forms","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Aleksy Tralle, Maciej Bochenski","submitted_at":"2024-03-03T15:01:56Z","abstract_excerpt":"We solve the long standing problem of classification of standard compact Clifford-Klein forms of homogeneous spaces of simple non-compact real Lie groups under the extra assumption that $G$, $H$, $L$ are simple and absolutely simple. Then the result is that standard compact Clifford-Klein forms always arise from triples $(\\mathfrak{g},\\mathfrak{h},\\mathfrak{l})$ of real Lie algebras such that $\\mathfrak{h}\\subset\\mathfrak{g},\\mathfrak{l}\\subset\\mathfrak{g}$, $\\mathfrak{g}$ is simple and absolutely simple, $\\mathfrak{h},\\mathfrak{l}$ are (non-compact) reductive, $\\mathfrak{g}=\\mathfrak{h}+\\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.10539","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2403.10539/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"}