Affiliation:
1. College of Mathematical Science, Yangzhou University, Yangzhou 225002, China
Abstract
Let D(Rm,n(q)) be the Drinfeld double of Radford Hopf algebra Rm,n(q) and D(Hs,t) be the Drinfeld double of generalized Taft algebra Hs,t. Both D(Rm,n(q)) and D(Hs,t) have very symmetric structures. We calculate all Hopf automorphisms of D(Rm,n(q)) and D(Hs,t), respectively. Furthermore, we prove that the Hopf automorphism group AutHopf(D(Rm,n(q))) is isomorphic to the direct sum Zn⨁Zm of cyclic groups Zm and Zn, the Hopf automorphism group AutHopf(D(Hs,t)) is isomorphic to the semi-direct products k*⋊Zd of multiplicative group k* and cyclic group Zd, where s=td,k*=k\{0}, and k is an algebraically closed field with char (k)∤t.
Funder
Natural Science Foundation of Jiangsu Province
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