不定度规空间上等距算子的典范矩阵
Canonical matrices of isometric operators on indefinite inner product spaces
摘要：
本文给出F上向量空间上由非退化型B和线性算子A组成的对（A，B）满足B（Ax，Ay）=B（x，y）的典范矩阵：（i）F是特征不同于2的代数闭域或实封闭的域，B是对称或斜对称的;（ii）F是代数闭域或实封闭的域上的斜四元数域，B关于F上的任何非恒等对合是Hermitian或斜Hermitian的.我们使用一种方法，承认减少问题的分类任意系统的形式和线性映射的问题的分类表示的一些图。该方法描述于[V. V. Sergeichuk，Math. USSR-Izv. 31（1988）481-501]。
英文摘要：
We give canonical matrices of a pair (A,B) consisting of a nondegenerate form B and a linear operator A satisfying B(Ax,Ay)=B(x,y) on a vector space over F in the following cases: (i) F is an algebraically closed field of characteristic different from 2 or a real closed field, and B is symmetric or skew-symmetric; (ii) F is an algebraically closed field or the skew field of quaternions over a real closed field, and B is Hermitian or skew-Hermitian with respect to any nonidentity involution on F. We use a method that admits to reduce the problem of classifying an arbitrary system of forms and linear mappings to the problem of classifying representations of some quiver. This method was described in [V.V. Sergeichuk, Math. USSR-Izv. 31 (1988) 481-501].
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