On a certain class of prehomogeneous vector spaces
On a certain class of prehomogeneous vector spaces
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关于某类预齐次向量空间
DOI：
10.1016/0022-4049(87)90051-x
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发表时间：
1987
影响因子：
0.8
通讯作者：
J. Igusa
中科院分区：
文献类型：
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作者：
J. Igusa
取特征为0的域k，考虑（G，X）的集合，其中X= Aff n，G是GL（X）的连通不可约k-子群，G传递地作用在不可约超曲面的补Y上. Sato和Kimura对k= C的（G，X）的分类是经典的.我们将确定（G，X），使Gk是在Yk上传递的情况下，G分裂在k上，并存在一个四元数除k-代数。这是由数论所激发并应用于数论的;参见。发明。85（1986）1-29和Amer.J.Math.109（1987）1-34。
We take a field k of characteristic 0 and consider the set of (G, X) where X= Aff n and G is a connected irreducible k-subgroup of GL (X) acting transitively on the complement Y of an irreducible hypersurface. A classification of (G, X) for k= C by Sato and Kimura is classical. We shall determine (G, X) such that G k is transitive on Y k in the case where G splits over k and a quaternion division k-algebra exists. This has been motivated by and applied to number theory; cf. Invent. Math. 85 (1986) 1–29 and Amer. J. Math. 109 (1987) 1–34.