阿贝尔transvection群的不变量理论
Invariant theory of abelian transvection groups
摘要：
设$G$是一个有限群，它线性地作用在具有任意特征的域上的向量空间$V$上。如果不变环是由代数独立的齐次不变量生成的，则称其作用为{ \em余正则};如果满射$k[V]^G$ -线性映射$π:k[V]\to k[V]^G$存在，则{ \em直和性质}成立.证明了Chevalley-Shephard-Todd型定理。假设$G$是阿贝尔的，则动作是共正则的当且仅当$G$是由伪反射生成的，并且直接被加数性质成立。
英文摘要：
Let $G$ be a finite group acting linearly on the vector space $V$ over a field of arbitrary characteristic. The action is called {\em coregular} if the invariant ring is generated by algebraically independent homogeneous invariants and the {\em direct summand property} holds if there is a surjective $k[V]^G$-linear map $π:k[V]\to k[V]^G$. The following Chevalley--Shephard--Todd type theorem is proved. Suppose $G$ is abelian, then the action is coregular if and only if $G$ is generated by pseudo-reflections and the direct summand property holds.
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