Automorphism group of Green ring of Sweedler Hopf algebra

Let H 2 be Sweedler’s 4-dimensional Hopf algebra and r(H 2) be the corresponding Green ring of H 2. In this paper, we investigate the automorphism groups of Green ring r(H 2) and Green algebra F(H 2) = r(H 2)⊗ℤ F, where F is a field, whose characteristics is not equal to 2. We prove that the automorphism group of r(H 2) is isomorphic to K 4, where K 4 is the Klein group, and the automorphism group of F(H 2) is the semidirect product of ℤ2 and G, where G = F {1/2} with multiplication given by a · b = 1− a − b + 2ab.