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abstract: 'An arbitrary group action on an algebra $R$ results in an ideal $\mfr$ of $R$. This ideal $\mfr$ fits into the classical radical theory, and will be called the radical of the group action. If $R$ is a noetherian algebra with finite GK-dimension and $G$ is a finite group, then the difference between the GK-dimensionsof $R$ and that of $R/\mfr$ is called the pertinency of the group action. We provide some methods to find elements of the radical, which helps to calculate the pertinency of some special group actions. The $\mfr$-adic local cohomology of $R$ is related to the singularities of the invariant subalgebra $R^G$. We establish an equivalence between the quotient category of the invariant $R^G$ and that of the skew group ring $R*G$ through the torsion theory associated to the radical $\mfr$. With the help of the equivalence, we show that the invariant subalgebra $R^G$ will inherit certain Cohen-Macaulay property from $R$.'
address:
- 'He: Department of Mathematics, Hangzhou Normal University, Hangzhou Zhejiang 310036, China'
- 'Y. ZhangDepartment of mathematics and statistics, University of Hasselt, Universitaire Campus, 3590 Diepenbeek, Belgium'
author:
- 'Ji-Wei He and Yinhuo Zhang'
title: Local cohomology associated to the radical of a 