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arXiv · 1407.3746

Isomorphy Classes of $k$-Involutions of $\text{SO}(n, k,\beta)$, $n > 2$

Robert W. Benim·Christopher E. Dometrius·Aloysius G. Helminck·Ling Wu
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Abstract

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 characteristic $2$. We use these results to classify the isomorphy classes of $k$-involutions of $\text{SO}(n, k,\beta)$ for some bilinear forms and some fields $k$.

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BibTeXRIS

Robert W. Benim, Christopher E. Dometrius, Aloysius G. Helminck, Ling Wu. 2014-07-14. Isomorphy Classes of $k$-Involutions of $\text{SO}(n, k,\beta)$, $n > 2$. https://arxiv.org/abs/1407.3746

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