Gorenstein代数上的Hopf代数作用

Actions of Hopf Algebras on Gorenstein Algebras

令H是有限维Hopf代数,A是左H-模代数,本文证明了A是Gorenstein代数 的充分必要条件,AH也是Gorenstein代数的条件.它是Enochs E E.,Garcia J J.和del Rio A.关于群作用相应的理论的推广.同时给出A/AH是Frobenius扩张的条件.

Let H be a Hopf algebra and A an. H-module algebra. We prove that A is a Gorenstein algebra if and only if AH is a Gorenstein algebra. This extends the result of Enochs E E., Garcia J J. and del Rio A. for group actions. We also give a condition under which A/AH is a Frobenius extension.