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arXiv · 1407.3784

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

Robert W. Benim·Aloysius G. Helminck·Farrah Jackson
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Abstract

A first characterization of the isomorphism classes of $k$-involutions for any reductive algebraic groups defined over a perfect field was given by Helminck in 2000 using $3$ invariants. In 2004, Helminck, Wu, and Dometrius gave a full classification of all 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 build on these results to develop a detailed characterization of the involutions of $\text{SP}(2n, k)$. We use these results to classify the isomorphy classes of involutions of $\text{SP}(2n, k)$ where $k$ is any field not of characteristic 2.

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BibTeXRIS

Robert W. Benim, Aloysius G. Helminck, Farrah Jackson. 2014-07-14. Isomorphy Classes of Involutions of $\text{SP}(2n, k)$, $n>2$. https://arxiv.org/abs/1407.3784

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