Given a finite dimensional selfinjective quiver algebra A over a finite field (or more generally an arbitrary field). Whats the best way to check if the algebra A has a Hopf algebra structure or not? If we assume the field to be finite it is a finite problem, so there might be some good algorithm? Note that there is a topic with the same question for not necessary finite dimensional algebra. But quiver algebras are much more special and maybe one can find stronger statements. For example the quiver algebra with 1 loop x and relations x^2=0 is a Hopf algebra iff the field has characteristic two. Is there a classification for small dimensions(maybe up to 100) of local finite dimensional (quiver) Hopf algebras?