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| AUTOMORPHISMS OF $\[SL(2,K)\]$ OVER SKEW FIELDS |
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Citation： |
Wu Xiaolong.AUTOMORPHISMS OF $\[SL(2,K)\]$ OVER SKEW FIELDS[J].Chinese Annals of Mathematics B,1988,9(4):436~441 |
| Page view： 944
Net amount： 638 |
Authors： |
Wu Xiaolong; |
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| Abstract： |
In this paper, the author proves the following result
Let $K$ be a skew field and $\[\Lambda \]$ be an automorphism of $\[SL(2,K)\]$. Then there exists
$\[A \in GL(2,K)\]$, an automorphism $\[\sigma \]$ or an anti-automorphism $\[\tau \]$ of $\[K\]$, such that $\[\Lambda \]$ is of the form
$$\[\Lambda X = A{X^\sigma }{A^{ - 1}}\]$$ for all $$\[X \in SL(2,K)\]$$
or
$$\[\Lambda X = A{({X^{{\tau _1}}})^{ - 1}}{A^{ - 1}}\]$$ for all $$\[X \in SL(2,K)\]$$
where $\[{X^\sigma },{X^\tau }\]$ are the matrices obtained by applying $\[\sigma \]$, $\[\tau \]$ on X respectively and $\[{X^'}\]$ is the transpose of X. |
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