关于含p^2维单子余代数的余半单Hopf代数

On cosemisimple Hopf algebras contains simple subcoalgebra of dimension p^2

设H是代数闭域K上的有限维余半单Hopf代数,charK=0.如果H具有型l∶1+m∶2+1∶5+…,则5│di mH;如果H具有型l∶1+m∶2+…+1∶pn+…,n∈N+,p为素数,则p│di mH.

Let H be a finite dimensional and cosemisimple Hopf algebra over an algebrically closed field K, andK has characteristic 0. If H has type. l∶1＋m∶2＋1∶5＋…, then 5｜dim H; if Hdoesnot contain 9-dimensional simple subcoalgebra and has type ： l∶1＋m∶2＋…＋1∶pn＋…,n∈N＋, p is a prime, then P ｜ dim H.