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Dissertation/Thesis Abstract

Isomorphy Classes of Involutions of SO(n, k, beta) and SP(2n, k) where n > 2
by Benim, Robert Wayne, Ph.D., North Carolina State University, 2014, 110; 3584003
Abstract (Summary)

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.

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