Gorenstein homological properties for Hopf--Galois extensions
Volume 157 / 2019
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.
