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Title: | Cohen-Macaulay invariant subalgebras of Hopf dense Galois extensions | Authors: | He, Jiwei ZHANG, Yinhuo |
Issue Date: | 2019 | Publisher: | American Mathematical Society | Source: | Andruskiewitsch, Nicolás; Nikshych, Dmitri (Ed.). Tensor Categories and Hopf Algebras, American Mathematical Society,p. 119-135 | Series/Report: | Contemporary Mathematics | Series/Report no.: | 728 | Abstract: | Let H be a semisimple Hopf algebra, and let R be a noetherian left H-module algebra. If R=RH is a right H -dense Galois extension, then the invariant subalgebra RH will inherit the AS-Cohen-Macaulay property from R under some mild conditions, and R, when viewed as a right RH-module, is a Cohen-Macaulay module. In particular, we show that if R is a noetherian complete semilocal algebra which is AS-regular of global dimension 2 and H = kG for some nite subgroup G Aut(R), then all the indecomposable Cohen- Macaulay module of RH is a direct summand of RRH, and hence RH is Cohen- Macaulay- nite, which generalizes a classical result for commutative rings. The main tool used in the paper is the extension groups of objects in the corresponding quotient categories. | Notes: | He, JW (reprint author), Show less Hangzhou Normal Univ, Dept Math, Hangzhou 310036, Zhejiang, Peoples R China. jwhe@hznu.edu.cn; yinhuo.zhang@uhasselt.be | Keywords: | Hopf dense Galois extension, quotient category, Cohen-Macaulay module. | Document URI: | http://hdl.handle.net/1942/28366 | Link to publication/dataset: | http://www.ams.org/cgi-bin/journals/myoffprints.pl/conm14658.pdf | ISBN: | 978-1-4704-4321-4 | DOI: | 10.1090/conm/728/14658 | ISI #: | 000473292300006 | Category: | C1 | Type: | Proceedings Paper | Validations: | ecoom 2020 |
Appears in Collections: | Research publications |
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Cohen-Macaulay invariant subalgebras of Hopf dense Galois extensions.pdf Restricted Access | Published version | 270.49 kB | Adobe PDF | View/Open Request a copy |
densegaloiscm3.pdf Restricted Access | Peer-reviewed author version | 384.75 kB | Adobe PDF | View/Open Request a copy |
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