Automorphism group of Green ring of Sweedler Hopf algebra

Abstract

Let H₂ be Sweedler’s 4-dimensional Hopf algebra and r(H₂) be the corresponding Green ring of H₂. In this paper, we investigate the automorphism groups of Green ring r(H₂) and Green algebra F(H₂) = r(H₂) ⊗{}_{Z}F, where F is a field, whose characteristics is not equal to 2. We prove that the automorphism group of r(H₂) is isomorphic to K₄, where K₄ is the Klein group, and the automorphism group of F(H₂) is the semidirect product of Z₂ and G, where G= F \ {1/2} with multiplication given by a · b= 1− a − b+ 2ab.

Keywords

Automorphism group / Green ring / Green algebra / Sweedler Hopf algebra

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2016 Higher Education Press and Springer-Verlag Berlin Heidelberg