I am using this definition:

An

algebra of functions on a finite quantum group$\mathbb{G}$ is a finite dimensional $C^\ast$-Hopf algebra $A=:F(\mathbb{G})$.

I have the following (very well known --- folklore --- result)

(Classification Theorem)Let $A$ be the algebra of functions on a finite quantum group $\mathbb{G}$:

- if $A$ is commutative then $\mathbb{G}\cong \Phi(A)$.
- if $A$ is cocommutative then $A=F(\mathbb{G})\cong \mathbb{C} \Phi(A)=:F(\widehat{\Phi(A)})$.

Here $\Phi(A)$ is the set of characters on $A$.

I want to reference these results but am struggling somewhat to find good, old, authoritative references. Any help would be appreciated.