The Hopf Automorphism Group of Two Classes of Drinfeld Doubles.

Let D (R m , n (q)) be the Drinfeld double of Radford Hopf algebra R m , n (q) and D (H s , t) be the Drinfeld double of generalized Taft algebra H s , t . Both D (R m , n (q)) and D (H s , t) have very symmetric structures. We calculate all Hopf automorphisms of D (R m , n (q)) and D (H s , t) , respectively. Furthermore, we prove that the Hopf automorphism group A u t H o p f (D (R m , n (q))) is isomorphic to the direct sum Z n ⨁ Z m of cyclic groups Z m and Z n , the Hopf automorphism group A u t H o p f (D (H s , t)) is isomorphic to the semi-direct products k * ⋊ Z d of multiplicative group k * and cyclic group Z d , where s = t d , k * = k \ { 0 } , and k is an algebraically closed field with char (k) ∤ t . [ABSTRACT FROM AUTHOR]