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

Tijdschriftbijdrage - Tijdschriftartikel

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 R-G. 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 R-G will inherit certain a Cohen-Macaulay property from R.
Tijdschrift: ISRAEL JOURNAL OF MATHEMATICS
ISSN: 0021-2172
Issue: 1
Volume: 231
Pagina's: 303 - 342
Jaar van publicatie:2019
BOF-keylabel:ja
IOF-keylabel:ja
BOF-publication weight:1
CSS-citation score:2
Auteurs:International
Authors from:Higher Education
Toegankelijkheid:Open