中文摘要：

令H为有限维Hopf代数且A为固定域k上的代数,AB为H-cleft扩张.利用cleft扩张和交叉积间的关系,证明了当H半单时,在cleft扩张下左余纯投射维数是不变的,并给出了A与B的QF性质.

英文摘要：

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 His semisimple.At the same time,QF properties about Aand B was investigated based on the assumption that ABis H-cleft.