摘要
Let H be a finite-dimensional Hopf algebra and assume that both H and H* are semisimple.The main result of this paper is to show that the representation dimension is an invariant under cleft extensions of H,that is,rep.dim(A) = rep.dim(A# σ H).Some of the applications of this equality are also given.
Let H be a finite-dimensional Hopf algebra and assume that both H and H＊ are semisimple. The main result of this paper is to show that the representation dimension is an invariant under cleft extensions of H, that is, rep.dim（A） = rep.dim（A^CaH）. Some of the applications of this equality are also given.
基金
partially supported by the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20100091110034)
National Natural Science Foundation of China(Grant Nos. 10771095, 10801069)
the Natural Science Foundation of Jiangsu Province of China (Grant No.BK2010047)
关键词
HOPF
代数和
有限维
半单
representation dimension, finite representation type, crossed product
