度为n的余半单Hopf代数的表示

Representation of Degree n for Cosemisimple Hopf Algebras

设H是代数闭域k上的余半单Hopf代数,n为正奇数.如果H除了含有一个维数为n2的单子余代数外,只含有维数不超过(2n-1)2的奇维数的单子余代数,且这些单子余代数的维数均不相同,则H或者包含一个阶为3,或5,或7,…,或n的群样元,或者存在一个n维自共轭基元xn,使得x2n=1+x3+x5+…+x2n-1,其中x3,x5,…,x2n-1是g(H)的基,且|x3|=3,|x5|=5,…,|x2n-1|=2n-1.

Let H be a cosemisimple Hopf algebra over an algebrically closed field k and n an odd positive integer.It is shown that if H only has simple distinct subcoalgebra of odd dimension which is no more than(2n-1)~2 except that H has a simple subcoalgebra of dimension n^2,then H contains either a grouplike element of order 3 or 5,or 7,…,or n,or there is a n-dimension self conjugate basic element x_n with x^2_n=1+x_3+x_5+…+x_(2n-1),where x_3,x_5,…,x_(2n-1) are basic elements of g(H) with ｜x_3｜=3,｜x_5｜=5,…,(｜x_(2n-...