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Gorenstein homological properties for Hopf--Galois extensions

Volume 157 / 2019

Xiaoyan Zhou, Tao Yang Colloquium Mathematicum 157 (2019), 203-212 MSC: Primary 16S40; Secondary 16E65. DOI: 10.4064/cm7525-6-2018 Published online: 12 April 2019

Abstract

Let $H$ be a semisimple Hopf algebra over a field $k$ and $A/B$ be a right $H$-Galois extension. We establish a relationship between several Gorenstein homological dimensions of $A$ and $B$ and we characterize when the category of finitely generated Gorenstein projective $A$-modules is abelian. As applications, we obtain some relations for crossed products and smash products.

Authors

  • Xiaoyan ZhouCollege of Science
    Nanjing Agricultural University
    Nanjing, Jiangsu 210095, P.R. China
    e-mail
  • Tao YangCollege of Science
    Nanjing Agricultural University
    Nanjing, Jiangsu 210095, P.R. China
    e-mail

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