弱Hopf Galois扩张的Cotorsion维数

Cotorsion Dimension of Weak Hopf Galois Extensions

考虑在Ext群上构造Grothendieck谱序列揭示弱Hopf Galois扩张的cotorsion维数.设H为有限维弱Hopf代数,A/B为弱H-Galois扩张,给出A,B的左cotorsion维数与H的右整体维数之间的关系,并讨论当B为可换的或H*为半单时,A,B的左cotorsion维数的性质.

We consider and construct a Orothendieck spectral sequence on me Ext groups to reveal the cotorsion dimensions of weak Hopf-Galois extensions. Let H be a finite dimensional weak Hopf algebra and A/B a weak H-Galois extension, we give the relationship between the left eotorsion dimensions of A,B and the right global dimensions of H, and discuss the properties of the left cotorsion dimensions of A.B when B is commutative or H＂ is semisimple.