Abstract:

Using the language of cogroupoids, we gave the relation between the global dimension of a Hopf algebra and the Hochschild dimensions of its HopfGalois objects. It is shown that the Hochschild dimensions of HopfGalois objects of H are at most d if H is a Hopf algebra with global dimension d.

Key words: Hopf algebra, HopfGalois object, global dimension, Hochschild dimension