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| THE AUTOMORPHISMS OF NON—DEFECTIVEORTHOGONAL GROUPS $\[{\Omega _S}(V)\]$ AND $\[O_s^'\]$IN CHARACTERISTIC 2 |
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Citation： |
Li Fuan.THE AUTOMORPHISMS OF NON—DEFECTIVEORTHOGONAL GROUPS $\[{\Omega _S}(V)\]$ AND $\[O_s^'\]$IN CHARACTERISTIC 2[J].Chinese Annals of Mathematics B,1986,7(1):1~13 |
| Page view： 977
Net amount： 893 |
Authors： |
Li Fuan; |
Foundation： |
Institute of Mathematics, Academia Sinica, Beijing, China. |
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| Abstract： |
Let $V$ be a non-defective S-dimensional quadratic space over a field $F$ of characteristic 2, $\[F \ne {F_2}\]$. We prove that if there is an exceptional automorphism of either $\[{\Omega _S}(V)\]$ or $\[O_S^'(V)\]$ then $\[{V^\alpha }\]$ has a Cayley algebra structure for some $\[\alpha \]$ in F. Moreover, every exceptional automorphism of $\[O_S^'(V)\]$ has exactly one of the following forms:
$$\[{\varphi _1} \circ {\Phi _g}or{\varphi _2} \circ {\Phi _g}\]$$
where $\[{\Phi _g}\]$ is an automorphism of $\[O_S^'(V)\]$ given by conjugation by a semilinear automorphism of V which preserves the quadratic structure, and $\[{\varphi _1}\]$ and $\[{\varphi _2}\]$ are the automorphisms induced by triality principle. Every exceptional automorphism of $\[{\Omega _S}(V)\]$ is the restriction of a unique exceptional automorpliism of $\[O_S^'(V)\]$. |
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