Abstract:

Let H be a finite dimensional Hopf algebra and A be an algebra over a fixed field k, using the relations between cleft extension and crossed product, we proved that the left copure projective dimension is invariant under cleft extensions when H is semisimple. At the same time, QF properties about A and B was investigated based on the assumption that AB is Hcleft.

Key words: cleft extension, copure projective dimension, QF ring