东南大学学报（英文版）2020，Vol.36Issue(4)：483-488,6.DOI:10.3969/j.issn.1003-7985.2020.04.014
弱Hopf-Galois扩张的Gorenstein维数
Gorenstein dimensions for weak Hopf-Galois extensions
摘要
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 A(○)B-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.关键词
弱Hopf代数/积分/弱Hopf-Galois扩张/Gorenstein维数Key words
weak Hopf algebra/integral/weak Hopf-Galois extension/Gorenstein dimension分类
数理科学引用本文复制引用
王忠伟..弱Hopf-Galois扩张的Gorenstein维数[J].东南大学学报（英文版）,2020,36(4):483-488,6.基金项目
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 Sci-ence Foundation of Jiangsu Province(No.BK20150113). （No.11601203）
