余半单Hopf代数的素数维余表示

Co-representations of prime dimension for cosemisimple Hopf algebras

设k是特征为0的代数闭域,H为k上的有限维余半单Hop f代数.首先证明了如果H具有型l∶1+m∶2+1∶3+…,则3整除H的维数;其次证明了如果H具有型l∶1+m∶2+…+1∶p+…,且H没有9维的单子余代数,则p整除H的维数,其中p为素数.

Let H be a cosemisimple Hopf algebra over an algebraically closed field k of characteristic zero. This paper shows that if H is of type l： 1 ＋m ： 2＋ 1 ： 3＋…, then its dimension is divisible by 3. It also shows if H is of type l ： 1＋m： 2＋…＋1： p＋…, and H does not contain simple subcoalgebras of dimension 9, then p divides the dimension of H,where p is prime.