2014/07/14 by Robert W. Benim, Christopher E. Dometrius, Benim, Robert W. +5 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #math.RT
paper · pdf · doi:10.48550/arxiv.1407.3746
43 Pages
openalex publication_date 2014/07/14 · arxiv created 2015/01/02 · arxiv updated 2015/01/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
A first characterization of the isomorphism classes of k-involutions for any reductive algebraic group defined over a perfect field was given in \citeHelm2000 using 3 invariants. In \citeHWD04,Helm-Wu2002 a full classification of all k-involutions on 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 SO(n,k,β), where β is any non-degenerate symmetric bilinear form and k is any field not of characteristic 2. We use these results to classify the isomorphy classes of k-involutions of SO(n, k,β) for some bilinear forms and some fields k.