Entwining结构和余代数Galois扩张的上同调  

Entwining structure and the cohomology of coalgebra Galois extension

作　　者：张素红[1] 

机构地区：[1]浙江工业大学理学院,杭州浙江310032

出　　处：《浙江工业大学学报》2006年第2期230-236,共7页Journal of Zhejiang University of Technology

摘　　要：在余代数Galois扩张A(B)C中,子代数B对其扩张代数A的结构具有决定作用.作者利用同调方法讨论了代数A和B的关系,证明了在适当条件下,代数A的同调维数不大于其子代数B的同调维数.更一般地,若(A,C)ψ为Entwining结构,作者分析了代数A与smash积C*op#RA之间的关系,若(A,C)ψ存在正规化积分,则smash积C*op#RA的同调维数不大于A的同调维数.特别地,若(A,C)ψ是中心Cleft余代数Galois扩张A(B)C的标准Entwining结构,则在适当条件下,smash积C*op#RA的同调维数不大于B的同调维数.In a coalgebra Galois extension A（B）^c, the structure of algebra A is determiaed by the sub-algebra B. The relations between the algebra A and the sub-algebra B is discussed in the view of homological algebra. It is proved that under some proper conditions, the homology dimension of A is not larger that the homology dimension of B. More generally, if （A,C）ψ is an Entwining structure, the relations between A and the smash product C^＊o^p # RA are discussed as well. If（A, C）ψ has a normal integral, then the homology dimension of the smash product C^＊o^p # RA is not larger than the homology dimension of A. In particular, if （A,C）ψ is canonical entwining structure of a center Cleft coalgebra Galios extension A（B）^c, then under some proper conditions, the homology dimension of C^＊op #RA is not larger than the homology dimension of B.

关 键 词：ENTWINING结构 余代数Galois扩张 同调双维数 

分 类 号：O153[理学—数学]