Hopf-Galois对象的Hochschild维数

Hochschild Dimensions of Hopf-Galois Objects

采用余群胚的语言讨论Hopf代数的整体维数与其Hopf-Galois对象的Hochschild维数间的关系.结果表明,如果Hopf代数H的整体维数是d,则H的Hopf-Galois对象的Hochschild维数≤d.

Using the language of cogroupoids,we gave the relation between the global dimension of a Hopf algebra and the Hochschild dimensions of its Hopf-Galois objects. It is shown that the Hochschild dimensions of Hopf-Galois objects of H are at most d if H is a Hopf algebra with global dimension d.