{"paper":{"title":"Curvature spectra of simple Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Andrzej Derdzinski, Swiatoslaw R. Gal","submitted_at":"2013-04-09T21:44:44Z","abstract_excerpt":"The Killing form \\beta\\ of a real (or complex) semisimple Lie group G is a left-invariant pseudo-Riemannian (or, respectively, holomorphic) Einstein metric. Let \\Omega\\ denote the multiple of its curvature operator, acting on symmetric 2-tensors, with the factor chosen so that \\Omega\\beta=2\\beta. The result of Meyberg [8], describing the spectrum of \\Omega\\ in complex simple Lie groups G, easily implies that 1 is not an eigenvalue of \\Omega\\ in any real or complex simple Lie group G except those locally isomorphic to SU(p,q), or SL(n,R), or SL(n,C) or, for even n only, SL(n/2,H), where p\\ge q\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2801","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"}