THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS

We study pointed graded self-dual Hopf algebras with a help of the dual Gabriel theorem for pointed Hopf algebras [15]. Quivers of such Hopf algebras are said to be self-dual. An explicit classication of self-dual Hopf quivers is obtained. We also prove that nite dimensional coradically graded pointed self-dual Hopf algebras are generated by group-like and skew-primitive elements as associative algebras. This partially justies a conjecture of Andruskiewitsch and Schneider [3] and may help to classify nite dimensional self-dual pointed Hopf algebras.