I am reading Natale's book [S. Natale, Semisolvability of semisimple Hopf algebras of low dimension, Mem. Amer. Math. Soc. 186 (2007), 123 pp.]. I can not understand a sentence "But this is not possible since ${\rm dim}A^{co q} = 9$....." from the proof of Theorem 12.2.1. In my option, there are severa possible values of ${\rm dim}A^{co q}$ since we do not know the exact order of $\eta$, and the sentence above holds true if and only if $\eta=2$. Who can explain it for me? Thanks a lot!
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One has that $dim(A)=dim\;(A^{co\; q})dim\;q(A)$. The claim is that $dim\;q(A)=2$, I don't know if $q$ restricted to $A$ is surjective. 

