# Is there a semi-simple complex finite-dimensional Hopf algebra that is not Kac?

It is said that a complex Hopf algebra (of finite dimension) is a
Kac algebra if it's a $${ rm C ^ { star}}$$algebra so that the comultiplication $$Delta$$ is a $$star$$-homomorphisme. Obviously, a Kac algebra (of finite dimension) is a semi-simple Hopf algebra, but what about the inverse:

Let $$H$$ to be a semi-simple complex finite-dimensional Hopf algebra.
Question: Is there a Kac algebra? $$K$$ isomorphic to $$H$$ as Hopf algebra?
If not, what is the smallest counterexample (for the dimension) and what is the main obstacle?