{"paper":{"title":"Galois cohomology of real semisimple groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.NT"],"primary_cat":"math.GR","authors_text":"Dmitry A. Timashev, Mikhail Borovoi","submitted_at":"2015-06-20T15:03:56Z","abstract_excerpt":"Let G be a connected, compact, semisimple algebraic group over the field of real numbers R. Using Kac diagrams, we describe combinatorially the first Galois cohomology sets H^1(R,H) for all inner forms H of G. As examples, we compute explicitly H^1 for all real forms of the simply connected group of type E_7 (which has been known since 2013) and for all real forms of half-spin groups of type D_{2k} (which seems to be new)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06252","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"}