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I'm huge confused!

There is nonzero primitive element in finite dimensional pointed hopf algebra over complex field???

I find in several articles,it is said that a is primitive,so a=0.

I will appreciate if someone can give me some clue.

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If $x$ is a primitive element in a Hopf algebra over a field of characteristic $0$, then $1$, $x$, $x^2$, ... are linearly independent over the field (unless $x=0$), so the Hopf algebra cannot be finitely-dimensional. – darij grinberg Oct 7 '11 at 16:06
(Tell me if you want the proof.) – darij grinberg Oct 7 '11 at 16:07
Usually, most questions are happy enough with one question mark. – Mariano Suárez-Alvarez Oct 7 '11 at 18:13

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