A first characterization of the isomorphism classes of k-involutions for any reductive algebraic groups defined over a perfect field was given in [Hel2000] using 3 invariants. In [HWD2004] a classification of all 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 build on these results to develop a detailed characterization of the isomorphy classes of involutions of SO(,and SP(2n, k). We use these results to begin a classification of the isomorphy classes of involutions of SO(n, k, β) and SP(2 n, k) where k is any field not of characteristic 2.
|School:||North Carolina State University|
|School Location:||United States -- North Carolina|
|Source:||DAI-B 75/10(E), Dissertation Abstracts International|
|Keywords:||Involutions, Orthogonal groups, Symmetric k-varieties, Symmetric spaces, Symplectic groups|
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