# Non-cosemisimple duals of pointed Hopf algebras

I take the following quote from an answer to this question

A Hopf algebra is called pointed if all its simple left (or right) comodules are one-dimensional. The quantized enveloping algebras and Lusztig's small quantum groups are examples of pointed Hopf algebras.

The finte/restricted Hopf duals of quantized enveloping algebras are all cosemisimple. Does this happen in general, or are the duals of all pointed Hopf algebras cosemisimple?

No way, doc! Take a finite $$p$$-group $$G$$. Let $${\mathbb F}$$ be a field of characteristic $$p$$. The group algebra $${\mathbb F}G$$ is as pointed as it gets. But its dual $${\mathbb F}G^{\ast}$$ is not cosemisimple because $${\mathbb F}G$$ is not semisimple.