  We contribute to the classification of Hopf algebras with finite
Gelfand-Kirillov dimension, GK-dimension for short, through the study of
Nichols algebras over Q 8 ,the quaternion group . We find all the irreducible
Yetter-Drinfeld modules V over Q 8 , and determine which Nichols algebras B(V )
of V are finite GK-dimensional, and which Nichols algebras B(V ) of V are
finite dimensional.
