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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/28366

Authors: He, Jiwei
Zhang, Yinhuo
Issue Date: 2019
Publisher: American Mathematical Society
Citation: 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
URI: http://hdl.handle.net/1942/28366
Link to publication: http://www.ams.org/cgi-bin/journals/myoffprints.pl/conm14658.pdf
DOI: 10.1090/conm/728/14658
ISI #: 000473292300006
ISBN: 978-1-4704-4321-4
Category: C1
Type: Proceedings Paper
Appears in Collections: Research publications

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