{"paper":{"title":"Klein Four subgroups of Lie Algebra Automorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Jing-Song Huang, Jun Yu","submitted_at":"2011-08-10T12:51:45Z","abstract_excerpt":"By calculating the symmetric subgroups $\\Aut(\\fru_0)^{\\theta}$ and their involution classes, we classify the Klein four subgroups $\\Gamma$ of $\\Aut(\\fru_0)$ for each compact simple Lie algebra $\\fru_0$ up to conjugation. This leads to a new approach of classification of semisimple symmetric pairs and $\\bbZ_2\\times \\bbZ_2$-symmetric spaces. We also determine the fixed point subgroup $\\Aut(\\fru_0)^\\Gamma$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2397","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"}