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http://hdl.handle.net/1942/28737
Title: | Local cohomology associated to the radical of a group action on a noetherian algebra | Authors: | He, Ji-Wei ZHANG, Yinhuo |
Issue Date: | 2019 | Publisher: | HEBREW UNIV MAGNES PRESS | Source: | ISRAEL JOURNAL OF MATHEMATICS, 231(1), p. 303-342 | 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 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. | Notes: | [He, Ji-Wei] Hangzhou Normal Univ, Dept Math, Hangzhou 310036, Zhejiang, Peoples R China. [Zhang, Yinhuo] Univ Hasselt, Dept Math & Stat, Univ Campus, B-3590 Diepenbeek, Belgium. | Document URI: | http://hdl.handle.net/1942/28737 | ISSN: | 0021-2172 | e-ISSN: | 1565-8511 | DOI: | 10.1007/s11856-019-1855-9 | ISI #: | 000470717200010 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2020 |
Appears in Collections: | Research publications |
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he 1.pdf Restricted Access | Published version | 292.12 kB | Adobe PDF | View/Open Request a copy |
localcohom4.pdf | Peer-reviewed author version | 460.1 kB | Adobe PDF | View/Open |
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