关于扭Hopf代数的一些注记

A Note on Twisted Hopf Algebras

中文关键词:  Hopf代数  扭Hopf代数  投射维数  整体维数.

英文关键词:Hopf algebras  twisted Hopf algebras  projective dimension  global dimension.

中文摘要:

      本文证明了扭Hopf代数对极的一些性质.同时还证明了扭Hopf代数的分次整体维数正是平凡模k的分次投射维数,也等于k的投射维数.

英文摘要:

      In this paper, we get some properties of the antipode of a twisted Hopf algebra. We proved that the graded global dimension of a twisted Hopf algebra coincides with the graded projective dimension of its trivial module $k$, which is also equal to the projective dimension of $k$.