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[1] Wang Zhongwei,. Gorenstein dimensions for weak Hopf-Galois extensions [J]. Journal of Southeast University (English Edition), 2020, 36 (4): 483-488. [doi:10.3969/j.issn.1003-7985.2020.04.014]
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Gorenstein dimensions for weak Hopf-Galois extensions()
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
36
Issue:
2020 4
Page:
483-488
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2020-12-20

Info

Title:
Gorenstein dimensions for weak Hopf-Galois extensions
Author(s):
Wang Zhongwei
School of Mathematics, Southeast University, Nanjing 211189, China
School of Science, Jinling Institute of Technology, Nanjing 211169, China
Keywords:
weak Hopf algebra;  integral;  weak Hopf-Galois extension;  Gorenstein dimension
PACS:
O153.3
DOI:
10.3969/j.issn.1003-7985.2020.04.014
Abstract:
The representation of weak Hopf algebras is studied by investigating the Gorenstein dimensions of weak Hopf algebras and weak Hopf-Galois extensions. Let H be a weak Hopf algebra with a bijective antipode, A a weak right H-comodule algebra and B the H-coinvariant subalgebra of A. First, some properties of Gorenstein projective H-modules in the representation category are studied, and the fact that Gorenstein global dimension of H is the same as the Gorenstein projective dimension of its left unital subalgebra is demonstrated. Secondly, by applying the integral theory of weak Hopf algebras, on the one hand, a sufficient and necessary condition that a projective A-module is a projective B-module is given; on the other hand, the separability of the functor AB- and that of the restriction of scalar function B(-)are described, respectively. Finally, as a mean result, the Gorenstein global dimension of a weak Hopf-Galois extension is investigated under the condition that H is both semisimple and cosemisimple.

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Memo

Memo:
Biography: Wang Zhongwei(1984—), male, doctor, associate professor, wangzhongwei@jit.edu.cn.
Foundation items: The National Natural Science Foundation of China(No.11601203), the China Postdoctoral Science Foundation(No.2018M642128), Qing Lan Project of Jiangsu Province, the Natural Science Foundation of Jiangsu Province(No.BK20150113).
Citation: Wang Zhongwei. Gorenstein dimensions for weak Hopf-Galois extensions[J].Journal of Southeast University(English Edition), 2020, 36(4):483-488.DOI:10.3969/j.issn.1003-7985.2020.04.014.
Last Update: 2020-12-20