Local cohomology associated to the radical of a group action on a noetherian algebra View Full Text


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Article Info

DATE

2019-04-01

AUTHORS

Ji-Wei He, Yinhuo Zhang

ABSTRACT

An arbitrary group action on an algebra R results in an ideal r of R. This ideal r 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-dimensions of R and that of R/r 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 r-adic local cohomology of R is related to the singularities of the invariant subalgebra RG. We establish an equivalence between the quotient category of the invariant subalgebra RG and that of the skew group ring R * G through the torsion theory associated to the radical r. With the help of the equivalence, we show that the invariant subalgebra RG will inherit certain a Cohen–Macaulay property from R. More... »

PAGES

1-40

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Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s11856-019-1855-9

DOI

http://dx.doi.org/10.1007/s11856-019-1855-9

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https://app.dimensions.ai/details/publication/pub.1113175350


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