{"paper":{"title":"Isomorphy Classes of $k$-Involutions of $\\text{SO}(n, k,\\beta)$, $n > 2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Aloysius G. Helminck, Christopher E. Dometrius, Ling Wu, Robert W. Benim","submitted_at":"2014-07-14T17:56:31Z","abstract_excerpt":"A first characterization of the isomorphism classes of $k$-involutions for any reductive algebraic group defined over a perfect field was given in \\cite{Helm2000} using $3$ invariants. In \\cite{HWD04,Helm-Wu2002} a full classification of all $k$-involutions on $\\text{SL}(n,k)$ for $k$ algebraically closed, the real numbers, the $p$-adic numbers or a finite field was provided. In this paper, we find analogous results to develop a detailed characterization of the $k$-involutions of $\\text{SO}(n,k,\\beta)$, where $\\beta$ is any non-degenerate symmetric bilinear form and $k$ is any field not of cha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3746","kind":"arxiv","version":2},"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"}