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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.
| Advisor: | Helminck, Aloysius |
| Commitee: | |
| School: | North Carolina State University |
| Department: | Mathematics |
| School Location: | United States -- North Carolina |
| Source: | DAI-B 75/10(E), Dissertation Abstracts International |
| Source Type: | DISSERTATION |
| Subjects: | Mathematics |
| Keywords: | Involutions, Orthogonal groups, Symmetric k-varieties, Symmetric spaces, Symplectic groups |
| Publication Number: | 3584003 |
| ISBN: | 978-1-303-99731-0 |
