Polynomial Separating Algebras and Reflection Groups

2013/07/29 by Reimers, Fabian
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1307.7522

Abstract

This note considers a finite algebraic group G acting on an affine variety X by automorphisms. Results of Dufresne on polynomial separating algebras for linear representations of G are extended to this situation. For that purpose, we show that the Cohen-Macaulay defect of a certain ring is greater than or equal to the minimal number k such that the group is generated by (k+1)-reflections. Under certain rather mild assumptions on X and G we deduce that a separating set of invariants of the smallest possible size n = dim(X) can exist only for reflection groups.

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