{"paper":{"title":"Notes on \"Einstein metrics on compact simple Lie groups attached to standard triples\"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Huibin Chen, Zhiqi Chen","submitted_at":"2017-01-06T18:12:09Z","abstract_excerpt":"In the paper \"Einstein metrics on compact simple Lie groups attached to standard triples\", the authors introduced the definition of standard triples and proved that every compact simple Lie group $G$ attached to a standard triple $(G,K,H)$ admits a left-invariant Einstein metric which is not naturally reductive except the standard triple $(\\Sp(4),2\\Sp(2),4\\Sp(1))$. For the triple $(\\Sp(4),2\\Sp(2),4\\Sp(1))$, we find there exists an involution pair of $\\sp(4)$ such that $4\\sp(1)$ is the fixed point of the pair, and then give the decomposition of $\\sp(4)$ as a direct sum of irreducible $\\ad(4\\sp("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01713","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"}