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Invariant Theory of Abelian Transvection Groups

Published online by Cambridge University Press:  20 November 2018

Abraham Broer
Abraham Broer*
Affiliation:
Département de mathématiques et de statistique, Université de Montréal, Montréal, QC H3C 3J7 e-mail: broera@dms.umontreal.ca
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Abstract

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Let $G$ be a finite group acting linearly on the vector space $V$ over a field of arbitrary characteristic. The action is called coregular if the invariant ring is generated by algebraically independent homogeneous invariants, and the direct summand property holds if there is a surjective $k{{[V]}^{G}}$-linear map $\pi \,:\,k[V]\,\to \,k{{[V]}^{G}}$.

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.

Keywords

13A50
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 53 , Issue 3 , 01 September 2010 , pp. 404 - 411
Copyright
Copyright © Canadian Mathematical Society 2010

References

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