Hopf代数的冲积的弱整体维数

摘要

Let H be a finite dimensional Hopf algebra and A a commutative H-module algebra. We prove that the smash product A#H is of the same weak global homological dimension as A, provided that H* is unimodular and there is a trace one element in A.%设H是有限维Hopf代数,A是交换的H-模代数.当H*是幺模且A中存在迹为1的元素时,本文证明冲积A#H与代数A的弱整体维数相等.