Invariant Theory of Abelian Transvection Groups

Localización: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 53, Nº 3, 2010, págs. 404-411
Idioma: inglés
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Resumen
- Let G be a finite group acting linearly on the vector space V over a field of arbitrary characteristic. The action is called \emph{coregular} if the invariant ring is generated by algebraically independent homogeneous invariants, and the \emph{direct summand property} holds if there is a surjective k[V]G-linear map :k[V]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.