Shephard–Todd–Chevalley Theorem for Skew Polynomial Rings
Shephard–Todd–Chevalley Theorem for Skew Polynomial Rings
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DOI：
10.1007/s10468-008-9109-2
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发表时间：
2008-06
影响因子：
0.6
通讯作者：
E. Kirkman;J. Kuzmanovich;James J. Zhang
中科院分区：
文献类型：
--
作者：
E. Kirkman;J. Kuzmanovich;James J. Zhang
我们证明了经典的Shephard-Todd-Chvalley定理的如下推广。设G是斜多项式环的分次代数自同构的有限群。当且仅当G是由拟反射生成的，则固定子环AG具有有限的整体维度。在这种情况下，固定子环AG同构于一个可能具有不同pij的斜多项式环.对于作用于一般量子多项式环上的阿贝尔群，也证明了该定理的一种形式.
We prove the following generalization of the classical Shephard–Todd–Chevalley Theorem. LetGbe a finite group of graded algebra automorphisms of a skew polynomial ring. Then the fixed subringAGhas finite global dimension if and only ifGis generated by quasi-reflections. In this case the fixed subringAGis isomorphic to a skew polynomial ring with possibly differentpij’s. A version of the theorem is proved also for abelian groups acting on general quantum polynomial rings.